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UNIVERSITY 
OF  FLORIDA 
LIBRARIES 


--«^w(e«T.f8S/Ullli 


THE    ECONOMICS    OF    LOCATION 


AUGUST   LOSCH 


The  Economics  of  Location 

TRANSLATED     FROM     THE     SECOND     REVISED      EDITION 

BY     WILLIAM     H.     WOGLOM     WITH     THE     ASSISTANCE     OF 

WOLFGANG    F.     STOLPER 


NEW    HAVEN    AND    LONDON: 

YALE    UNIVERSITY    PRESS 


^ 


C."^ 


Copyright,  1954,  by  Yale  University  Press. 

Seventh  printing,  1978. 

Printed  in  the  United  States  of  America  by 

The  Murray  Printing  Company, 

IVestford,  Massachusetts. 

All  rights  reserved.  This  book  may  not  be 

reproduced,  in  whole  or  in  part,  in  any  form 

(beyond  that  copying  permitted  by  Sections  loy 

and  108  of  the  U.S.  Copyright  Law  and  except  by 

reviewers  for  the  public  press),  without  written 

permission  from  the  publishers. 

Library  of  Congress  catalog  card  number:  52—9268 

ISBN:  0-300-00727-2 

Published  in  Great  Britain,  Europe,  Africa,  and 
Asia  (except  Japan)  by  Yale  University  Press, 
Ltd.,  London.  Distributed  in  Australia  and  New 
Zealand  by  Book  &  Film  Services,  Artarmon,  N.S.W., 
Australia;  and  in  Japan  by  Harper  &  Row,  Publishers, 
Tokyo  Office. 


^ 

^ 


Translator's  Note 


The  translator  gratefully  acknowledges  the  indispensable  help  ot  two 
distinguished  economists. 

Dr.  Edgar  M.  Hoover,  while  on  the  staff  of  the  President's  Council 
of  Economic  Advisers,  read  the  entire  translation  in  manuscript  and 
furnished  a  great  many  valuable  suggestions. 

Wolfgang  F.  Stolper,  professor  of  economics  at  the  University  of 
Michigan,  also  read  the  manuscript  through.  A  fellow  student  of  Losch 
under  Schumpeter,  in  Bonn,  Germany,  and  a  close  lifelong  friend  there- 
after, he  was  able  to  interpret  some  expressions  peculiar  to  the  author 
that  otherwise  might  have  remained  obscure. 

The  translator  has  profited  throughout,  too,  by  the  advice  and  assis- 
tance of  the  staff  of  the  Yale  University  Press. 

W.  H.  W. 

Teaneck,  New  Jersey,  May,  1952 


Grateful  acknowledgment  is  made   to   the  Social  Science   Research 
Council  for  a  grant  which  facilitated  the  translation. 


Digitized  by  the  Internet  Archive 

in  2010  with  funding  from 

Lyrasis  IVIembers  and  Sloan  Foundation 


http://www.archive.org/details/economicsoflocatOOIs 


August  Losch  in  Memoriam 


Written  amid  privations  and  war,  The  Economics  of  Location  bears 
witness  to  a  combination  of  rare  strength  of  character,  intellect,  and 
warmth  of  personality  in  its  author  which  is  not  frequently  found 
in  scientific  works  in  any  language. 

August  Losch  was  born  in  1906.  He  died  shortly  after  the  end 
of  hostilities  on  May  30,  1945,  at  least  partially  as  the  result  of  that 
very  strength  of  character  which  forbade  him  to  make  any  com- 
promises with  the  National  Socialist  regime.  He  never  even  con- 
sidered taking  a  government  or  academic  position  in  which  he 
would  have  had  to  swear  a  personal  oath  of  allegiance  to  Hitler. 
The  willingness  to  accept  a  professorship  after  the  war,  which  he 
expressed  in  the  foreword  to  the  second  edition  of  his  book,  speaks 
for  his  courage  as  well  as  for  his  solitude.  It  is  for  this  reason  that 
though  we  have  omitted  this  note  from  the  American  edition  we 
have  not  felt  free  to  change  any  of  the  many  passages  in  which  his 
love  for  his  homeland  of  Swabia  is  fervently  expressed.  For  what 
has  been  hypocrisy  in  many  others  who  turn  their  love  of  country 
to  account,  in  Losch  is  a  reminder  that  there  are  men  who  can  com- 
bine passion  with  intellect,  love  of  home  with  a  cosmopolitan  view. 

Even  a  glance  at  The  Economics  of  Location  is  enough  to  con- 
vince the  reader  that  its  author  was  an  extraordinary  personality. 
All  of  Losch's  work  is  original  in  a  double  sense  of  the  term.  He 
asked  significant  new  questions  and  he  added  significantly  to  the 
answers  given  by  others  to  older  questions.  Like  most  truly  original 
persons,  Losch  appreciated  the  contributions  of  others.  The  Eco- 
nomics of  Location  contains  an  immense  number  of  references  to 
other  works.  But  two  things  stand  out:  Losch  never  hesitated  to 
quote  anyone  whether  or  not  he  belonged  to  the  "  wrong  "  nation 
or  "  race  "—which  was  by  no  means  easy  at  the  time  he  was  writing 
this  book.  And  he  never  quoted  merely  to  criticize.  This  book,  a 
substantial  piece  of  work,  not  only  gives  credit  where  credit  is 
due;  it  shows  an  appreciation  of  the  achievement  of  others  without 
accepting  anything,  including  the  author's  own  contribution,  as 
final  truth.  Yet  no  man  had  more  passion  for  truth,  more  feeling 
for  the  fact  that  truth  must  come  before  originality. 

Losch's  first  publication  concerned  the  transfer  problem  and 


yjii  The  Economics  of  Location 

grew  out  of  a  seminar  paper.    His  first  major  piece  of  work  was  a 
booklet  about  the  economic  consequences  of  a  declining  population, 
perhaps  the  best  discussion  of  the  problem  in  terms  of  classical   (in 
the  sense  of  pre-Keynesian)   theory  that  exists.   The  subject  was  set 
as  a  prize  question  and  Losch  won  the  contest.   Because  he  believed 
in  personal  freedom,  including  the  taking  of  risks,  he  chose  to  pub- 
lish the  booklet  himself,  using  the  prize  money  for  the  purpose. 
That  book  and  his  next  major  work,  on  Population  Cycles  and 
Business  Cycles,  dealt  with  the  economics  of  population.   Both  show 
all  the  characteristics  of  a  modern  economist  who  attempts  to  fuse 
theory  and  facts  in  one  indissoluble  whole.  The  books  are  concisely 
written;  no  superfluous  introductions  ease  the  reader  into  the  subject 
matter.    Nor  does  Losch  spare  the  reader  concise  reasoning  or  a 
multitude  of  facts. 

It  may  not  be  without  interest  to  give  the  main  results  of  Losch's 
population  study  in  some  detail,  since  the  relation  of  population 
growth  and  business  cycles  has  aroused  new  interest  through  the 
Keynes-Hansen-Terborgh  discussion,  through  the  stagnation  thesis 
and  criticisms  of  it,  and  again  through  the  fact  that  the  forties  and 
early  fifties  have  been  a  period  of  prosperity  which  has  also  witnessed 
the  largest  absolute  increase  of  population  in  the  history  of  the 
United  States. 

The  question  whether  population  cycles  cause  business  cycles 
requires  different  answers,  according  to  Losch,  in  the  precapitalist 
and  the  capitalist  eras.  During  the  capitalist  era  population  move- 
ments are  neither  necessary  nor  sufficient  to  explain  the  fluctuations 
of  the  economy.  Nevertheless  Losch  establishes  the  fact  that  in 
Germany  industrial  production  as  a  rule  increased  quickly  following 
a  population  increase.  Indeed,  during  the  periods  1861-1913  and 
1923-33  he  finds  only  two  exceptions  to  this  relationship.  Since  the 
economic  development  of  growing  nations  takes  to  a  large  extent 
the  form  of  increased  housing  and  capital  equipment  for  the 
increased  numbers  of  people,  as  well  as  of  increased  amounts  of 
consumers'  goods,  it  is  not  unexpected  that  the  rhythm  of  population 
movements  and  of  business  cycles  should  largely  coincide.  Further- 
more, the  growth  of  the  economy  to  accommodate  a  growing  popu- 
lation entails  smaller  risks  than  the  adaptation  to  changes  brought 
about  by  technological  progress  and  the  creation  of  new  markets. 
Thus,  in  Losch's  own  words,  although  "  population  growth  does  not 
create  business  cycles,  it  shapes  their  course." 

This  kind  of  discussion  is  quite  familiar  today.  But  Losch  ante- 
dates the  Keynesian  discussion.   If  his  contribution  is  formulated  in 


August  LdscJi  in  Memoriam  "^ 

terms  of  any  one  particular  frame  of  reference,  it  is  in  terms  of 
Spiethoff's  or  perhaps  Schumpeter's  rather  than  Keynes'  theoretical 
language.  His  contribution  is  distinguished  by  solid  statistical 
verification  and  arguments  largely  missing  in  the  Anglo-American 
discussion. 

The  Economics  of  Location,  like  his  book  on  population  cycles, 
exhibits  the  characteristics  of  a  man  blessed  at  the  same  time  with 
originality  and  a  sense  of  tradition  and  history.  Losch  knew  and 
used  the  traditional  theories  of  location  from  von  Thiinen  on.  Yet 
he  succeeded  in  bringing  new  insights  even  to  so  well-developed  a 
theory  as  that  of  the  famous  Thunen  rings.  His  criticism  of  Alfred 
Weber's  location  theory  is  essentially  that  voiced  by  Schumpeter.^ 
Weber's  solution  is  in  terms  of  partial  equilibrium  theory  and  as 
such  is  a  brilliant  piece  of  work.  But  the  partial  equilibrium 
approach  means  that  among  the  other  things  which  have  to  be 
assumed  as  given  are  demand,  the  location  of  raw  materials,  and 
the  location  of  markets.  What  remains  to  be  accomplished,  there- 
fore, once  a  satisfactory  solution  of  the  partial  equilibrium  problem 
has  been  found,  is  the  development  of  a  general  equilibrium 
approach. 

This  is  precisely  one  of  Losch's  major  contributions.  He  had 
Ohlin's  and  Palander's  work  to  build  on,  and  gratefully  acknowl- 
edged both— in  spite  of  the  fact  that  he  was  already  working  out 
his  own  ideas  when  they  published  their  contributions.  It  is  never- 
theless fair  to  say  that  Losch  was  the  first  to  present  a  full  general 
equilibrium  system  describing  in  abstract  the  interrelationship  of 
all  locations.  To  be  sure,  he  did  not  go  beyond  counting  equations 
and  unknowns.  But  this  in  itself  is  a  major  achievement  which, 
in  its  precision,  had  eluded  his  intellectual  forebears.  Again  his 
achievement  sets  the  stage  for  the  next  step  in  the  development  of 
the  general  theory  of  location:  the  development  of  the  dynamics  of 
locations.  Lest  we  lose  patience  and  courage  it  may  be  well  to 
remember  that  it  was  over  sixty  years  before  dynamics  was  added 
to  the  Walrasian  system. 

Losch  himself  has  pointed  out  that  his  system  of  equations  shares 
the  weakness  of  any  general  theory  which  is  too  all-inclusive  to  be 
applicable.  This  was  one  of  the  reasons  why  he  developed  his  theory 
of  economic  regions.  However,  the  theoretical  framework  itself  is 
useful  for  a  number  of  problems  for  which  it  must,  of  course,  be 
narrowed  down  and  made  specific.  It  is  surely  no  accident  that 
one  of  the  most  useful  pieces  of  theoretical  and  empirical  research, 

1,  In  Schmollers  Jahrbuch,  XXXIV   (1910),  1356  ff. 


X  The  Economics  of  Location 

Leontief  s  input-output  analysis,  which  has  opened  up  entirely  new 
vistas,  is  based  on  the  most  general  Walrasian  system.  And  the 
application  of  input-output  analysis  to  regional  data,  attempted  by 
Isard,  for  the  same  reason  will  have  to  come  to  terms  with  the  general 
theory  of  location  which,  in  a  sense,  is  simply  the  application  of  the 
Walrasian  system  to  an  economy  in  which  distance  is  also  a  variable. 
Finally,  anyone  who  works  with  regional  economies  of  the  real  world 
knows  that  interregional  relationships  assume  greater  importance 
the  smaller  the  region  considered.  Any  theory  which  enables  the 
scholar  to  keep  these  mutual  relationships  in  mind  therefore  fulfills 
an  important  function  in  empirical  research, 

Losch's  discussion  of  the  nature  of  economic  regions  is  probably 
his  most  original  contribution.  To  be  sure,  here  too  he  has  in 
Ohlin  a  magnificent  predecessor.  Yet  there  are  enough  differences 
to  mark  Losch's  work  as  something  entirely  new.  The  novelty  could 
be  characterized  in  different  ways.  Losch  does  not  assume  his  region 
or  define  it,  for  example,  by  means  of  factor  mobility;  nor  does  he 
assume  the  existence  of  markets,  sources  of  raw  materials,  or  even 
transport  lines.  Instead  he  develops  the  structure  of  a  region,  that 
is,  the  interrelationship  of  all  relevant  variables,  with  a  minimum 
of  assumptions  which,  with  true  genius,  are  deliberately  chosen  to 
be  as  generalized  as  possible.  The  very  lack  of  realism  reminds  one 
of  the  theory  of  comparative  cost  which  also  substituted  for  the 
trivial  realism  that  grapes  could  not  be  grown  in  Scotland  the 
brilliant  proof  that  an  inefficient  producer  could  not  be  undersold 
in  all  goods. 

To  put  it  differently,  Losch  does  not  ask  for  the  definition  of 
a  region  by  means  of  which  to  analyze  it,  nor  does  he  search 
for  particular  characteristics.  His  region  is  not  defined  by  factor 
mobility— for  factor  mobility  is  also  permissible  between  regions— 
nor  by  "  homogeneity  "  nor  by  "  self-sufficiency,"  though  the  last 
and  possibly  also  the  first  of  these  characteristics  can,  after  his  dis- 
cussion of  the  nature  of  a  region,  be  read  into  it.  Instead  his 
question  concerns  the  interrelationship  of  individual  production 
and  consumption  units,  the  eventual  location  of  markets  and  pro- 
ducing centers,  of  transport  lines,  of  distribution  of  population  and 
cities,  all  to  be  simultaneously  and  mutually  determined.  What 
matters  is  the  complicated  structure,  the  Gestalt,  not  the  average 
characteristics  of  an  area.  The  relevance  of  these  ideas  to  the  prob- 
lems of  underdeveloped  countries  is  obvious,  and  their  application 
in  specific  cases  may  turn  out  to  be  extremely  useful. 

The  statistician  and  empirical  scholar  may  well  point  out  that 


AuguiC  Losch   in  Meinoiiain  xi 

Statistics  cannot  possibly  be  assembled  for  all  points  of  the  United 
States  but  must  of  necessity  be  combined  for  smaller  or  larger  areas. 
This  is  true  enough,  though  perhaps  less  true  than  it  seems  at  first, 
since  the  aggregations  themselves  are  based  on  the  detailed  indi- 
vidual data  originally  collected.  And  even  to  the  extent  to  which 
it  is  true,  it  is  less  damaging  than  at  first  appears.  The  bulk  of 
Losch's  book  consists  of  applications  of  his  ideas  to  data,  chiefly  to 
American  data.  This  alone  indicates  their  fruitfulness  for  empirical 
research.  But  again,  anyone  working  with  regional  data  knows  that 
little  can  be  done  with  the  data  of  a  single  region  in  isolation  with- 
out considering  interrelationships  with  other  areas.  The  income  of 
a  region  depends,  of  course,  on  its  productivity,  but  just  as  clearly 
on  the  prices  of  its  exports  and  imports.  As  soon  as  this  is  pointed 
out,  the  structure— industrial,  agricultural,  population,  capital,  etc.— 
again  becomes  of  paramount  importance.  In  a  similar  manner  inter- 
regional wage  differentials  cannot  be  understood  without  an  aware- 
ness of  the  structure  both  of  a  region  and  its  relationships  with  the 
outside  world. 

The  Economics  of  Location  is  not  easy  reading.  This  is  partly 
due  to  the  evident  pressure  under  which  it  was  written.  In  a  few 
places  it  may  be  because  important  passages  from  the  first  edition 
which  were  omitted  from  the  second  German  edition  to  save  space 
have  been  reinserted  in  the  American  edition  in  the  appropriate 
places.  But  basically  it  is  due  to  the  very  newness  of  the  ideas:  not 
enough  time  has  as  yet  elapsed  or  professional  discussion  taken  place 
since  the  publication  of  the  book  to  lead  to  simplification,  a  stream- 
lining as  it  were,  of  the  formulations.  Losch's  work  opens  up  new 
vistas  and  new  avenues  of  research.  No  greater  compliment  could 
be  paid  to  it  than  its  being  taken  up  where  Losch  left  off  and  carried 
on  to  new  formulations  and  achievements.  The  highest  praise  of 
this  book  will  be  if  in  the  future  it  can  be  said  that  the  work  it 
has  stimulated  has  made  it  obsolete. 

"Wolfgang  F.  Stolper 
Ann  Arbor,  Michigan 
1953 


Preface  to  First  Edition 


Just  as  the  theory  of  economic  development  considers  time,  so 
this  book  will  include  space  in  its  approach  to  economics,  not  only 
in  the  case  of  individual  problems,  as  has  been  done  before,  but 
throughout  the  entire  field.  It  proposes  to  view  all  economic 
activities  geographically.  In  principle  all  economic  theory  can  be 
reformulated  thus  from  a  spatial  aspect.  But  every  exploration  of 
new  territory  will  concentrate  first  on  the  investigation  of  what  is 
most  interesting.  I  have  been  less  interested  in  outlining  a  theory 
that  is  complete  than  one  that  is  capable  of  further  development; 
and  I  believe,  for  example,  that,  on  the  basis  of  the  theoretical 
foundation  given,  dynamics  could  easily  be  introduced  into  the 
spatial  picture.  If  the  fundamental  idea  of  the  work  is  sound, 
omissions  and  errors  in  details  should  not  weigh  too  heavily.  It  is 
of  little  importance,  too,  that  some  of  my  partial  results  have  already 
become  known  in  the  meantime,  since  I  have  written  this  book  not 
for  its  details  but  because  of  its  broad  view. 

Obviously  it  was  necessary  first  to  integrate  the  scattered  results  of 
previous  research  and— what  is  particularly  important  in  this  special 
field— bring  them  into  harmony  with  general  economic  theory.  But 
over  and  above  that,  this  investigation  develops  a  systematic  location 
theory,  a  new  theory  of  foreign  trade,  and  perhaps  the  first  general 
analysis  of  the  nature  of  economic  regions.  These,  Parts  II  and  III, 
are  the  kernel  of  the  whole  book. 

The  relation  of  the  present  investigations  to  my  previous  ones 
is  this:  Those  dealt  with  the  relations  between  peoples  and  the 
economy  whereas  this  treats  of  the  relations  between  space  and  the 
economy.  Or,  seen  from  the  standpoint  of  population,  the  subject 
there  was  its  development  in  time  and  here,  on  the  contrary,  its 
distribution  in  space. 

I  conceived  the  plan  of  the  present  work  ten  years  ago,  as  a 
young  student.  At  that  time  I  could  not  foresee  the  practical  interest 
that  these  questions  would  arouse  today,  or  that  the  underlying  prin- 
ciple of  the  book,  its  recognition  of  local  stability  in  the  widest 
sense,  for  which  I  then  thought  I  had  to  do  battle,  would  have 
prevailed  so  completely  in  the  meantime.  Throughout  this  whole 
period  I  have  never  discussed  the  basic  features  of  my  idea.  But 
just  because  I  was  so  sure  of  my  course,  at  first  instinctively  and 


xiv  The  Economics  of  Location 

then  more  and  more  consciously,  I  could  absorb  in  detail  so  much 
of  the  information  and  suggestions  that  streamed  in  upon  me  with- 
out losing  myself  in  a  welter  of  theories  or  facts.  It  is  therefore 
impossible  to  give  a  complete  list  of  all  those  who  assisted  in  my 
investigation  with  advice,  criticism,  or  information,  or  by  co- 
operating in  so  many  ways.  For  their  constant  readiness  to  help 
I  thank  first  of  all  my  teachers,  Arthur  Spiethoff,  in  Bonn;  Walter 
Eucken,  in  Freiburg;  and  Joseph  Schumpeter,  at  Harvard  University. 
My  obligation  is  especially  great  to  the  Rockefeller  Foundation, 
which  generously  made  possible  my  two  trips  of  investigation 
through  all  North  America,  and  the  publication  of  their  results. 
I  sincerely  thank,  also,  the  Paul  Stelzmann  Fund,  in  Freiburg,  for 
helping  me  through  a  critical  situation.  To  Professor  Wassily 
Leontief  I  am  indebted  for  valuable  suggestions,  and  mention  in 
gratitude  at  least  the  following  others:  Professors  Taussig,  Chamber- 
lin,  and  v.  Haberler  of  Harvard,  headquarters  for  my  American 
investigations;  the  members  of  the  Cowles  Commission  and  Profes- 
sors Roos  and  Hotelling,  with  whom  I  spent  a  never-to-be-forgotten 
summer  in  Colorado  Springs;  Professors  Evans  in  Berkeley;  Carver 
in  Minneapolis;  Hoover  in  Ann  Arbor;  Riefler,  then  in  Princeton, 
and  Whittlesey;  Spengler  in  Durham;  Dr.  Christaller  in  Freiburg; 
and  numerous  other  economists  and  geographers  at  the  universities 
already  mentioned  as  well  as  at  those  in  Chicago,  Baton  Rouge,  Iowa 
City,  and  Chapel  Hill.  I  received  the  warmest  cooperation  from  the 
Internal  Trade  Branch  of  the  Dominion  Bureau  of  Statistics,  in 
Ottawa,  and  the  Retail  Price  Division  of  the  Bureau  of  Labor 
Statistics,  in  Washington,  whose  director,  Mrs.  S.  Stewart,  took  special 
interest  in  the  question  of  regional  price  differences.  Dr.  Constantine 
E.  McGuire,  of  Washington,  opened  up  many  possibilities  to  me  in 
the  friendliest  manner.  Minister  Barton,  in  Ottawa,  and  Vice-Presi- 
dent Powell,  treasurer  Stewart,  and  other  officers  of  the  Federal 
Reserve  Banks  in  Minneapolis  and  St.  Louis;  Messrs.  McGregor,  of 
the  Dominion  Tariff  Board  (Ottawa) ,  Young,  of  the  Bureau  of 
Mines  (Washington) ,  Charles  L.  Horn  and  J.  Bell  of  Minneapolis, 
A.  Edwards,  F.  W.  Olin,  and  Col.  Jackson  of  St.  Louis,  not  to  men- 
tion many  other  officials,  librarians,  and  economists,  freely  gave  me 
information.  In  Germany  I  availed  myself  of  the  excellent  oppor- 
tunities for  work  at  the  Institut  fiir  Weltwirtschaft  in  Kiel.  I  shall 
still  have  an  opportunity  to  thank  a  few  persons  in  the  text,  but 
there  remain  many  more  whose  help  I  value  even  though  I  cannot 
call  them  by  name  here.  Last  but  not  least  I  thank  my  mother  and 
my  fiancee,  who  facilitated  the  accomplishment  of  this  wearisome 
task  at  great  personal  sacrifice. 


Preface  to  First  Edition  xv 

There  are  mathematical  calculations  in  this  book,  because  it  is 
reprehensible  not  to  trust  reason  and  rest  content  with  vague  words 
and  hazy  sentiments.  But  there  are  also  speculation  and  phi- 
losophizing where  the  frontiers  of  the  calculable  are  crossed,  and 
especially  where  the  meaning  of  the  whole  is  to  be  interpreted. 
As  for  mathematics,  I  have  neither  sought  nor  shunned  it,  but  have 
simply  employed  it  where  it  was  superior  to  other  methods.  He  who 
has  a  better  command  of  it  may  be  willing  to  forgive  me  for  the 
ponderous  presentation;  he  who  is  less  well  schooled  in  mathematics 
may  skip  the  dry  proof  if  only  he  accepts  the  results.  On  the  other 
hand,  nothing  was  further  from  my  mind  than  to  be  satisfied  with  a 
cold  mathematical  consideration.  This  would  resemble  a  mere  brick 
shell  that  is  not  yet  ready  for  occupation;  a  skeleton  without  flesh 
or  blood.  But  it  meant  giving  up  a  number  of  original  intentions, 
even  those  that  I  most  cherished.  Here,  indeed,  I  believe  it  is 
impossible  to  do  without  a  solid  foundation.  One  can  erect  a  large 
or  a  small  house  on  a  foundation,  adding  more  or  taking  away  to 
create  comfort;  but  building  materials  without  a  foundation  remain 
a  formless  mass.  This  is  sufficiently  proved  by  the  many  well-meant 
endeavors  to  achieve  a  living  science  immediately,  and  without  rigid 
thinking.  In  such  a  neglected  field  as  location  theory  it  required 
many  years  of  hard  work  before  even  a  tenable  intellectual  structure 
could  be  erected.  Yet  I  hope  that  even  in  its  objective  restraint  it 
testifies  to  a  sense  of  reality  and  to  a  belief. 

I  was  fortunate  in  being  able  to  develop  and  test  my  views 
through  the  more  readily  understandable  conditions  in  America. 
Though  a  foreigner  slips  more  easily  into  error,  my  presentation 
on  the  whole  may  show  even  the  American  reader  the  economy  of 
his  country  from  a  new  viewpoint,  and  thus  serve  in  some  small 
degree  to  express  my  thanks  for  the  help  and  hospitality  experienced 
there  in  a  hundred  different  ways. 

It  was  not  easy  for  me  largely  to  forego  the  attractive  task  of 
applying  what  had  thus  been  tested  to  our  more  complicated  German 
conditions  and  analyzing  the  pertinent  facts.  But  apart  from  all 
foreign  studies  and  the  wide  applicability  of  the  resulting  ideas,  my 
youthful  experiences  in  a  little  Swabian  town  constitute  the  real 
background  of  this  book.  I  am  convinced  that  we  rarely  learn  to 
know  any  conditions  as  intimately  as  those  among  which  we  grew  up. 
We  can  judge  with  certainty  only  a  small  understandable  and 
familiar  world  like  this,  and  we  transfer  the  findings  to  large 
problems  afterward.  My  Swabian  homeland  constitutes  such  a 
world  in  miniature,  if  any  economic  landscape  at  all  can  be  said 


xvi  The  Economics  of  Location 

to  do  so.  To  have  my  original  experiences  there  confirm  my  final 
theories  gives  me  a  real  sense  of  security,  and  so  I  dedicate  this 
book  to  the  land  of  my  birth,  the  land  that  I  love. 

August  Losch 

Heidenheim    (Wilrttemberg) 
Autumn,  1939 


Preface  to  the  Second  Edition 


The  favorable  reception  accorded  this  book,  long  since  out  of 
print,  beyond  the  circle  of  German  economists  and  even  abroad,^ 
in  other  sciences,  and  especially  among  practical  economists,  encour- 
aged my  resolve  to  publish  a  new  edition,  although  for  a  long  time 
conditions  prevented  me  from  making  many  of  the  changes  that  I 
should  have  liked  to  make.  Nevertheless  I  have  at  least  worked  out 
more  clearly  my  location  theory,  which  in  the  first  edition  was  merely 
a  preliminary  study;  added  some  new  material  on  geographic  price 
differences;  supplied  what  was  most  necessary  to  the  regional  plan- 
ning made  timely  by  the  war;  and  presented  the  transfer  problem 
in  better  form,  so  far  as  monetary  problems  relate  to  it.^  In  addition, 
those  who  are  familiar  with  the  first  edition  will  discover  new 
observations,  statistics,  and  illustrations  here  and  there.  Occasionally 
the  presentation  could  be  simplified,  but  nothing  decisive  would  be 
achieved:  the  indescribable  difficulties  under  which  the  book  was 
first  written  so  compressed  and  reduced  what  is  valid,  beyond  mere 
impressions,  that  only  he  who  studies  it  thoroughly  will  be  able 
fully  to  exhaust  its  contents. 

However,  a  few  hints  may  be  of  service  to  those  who  hurry 
through  it.  Entrepreneurs  may  be  especially  interested  in  pages 
396-420;  bankers  in  461-476  and  505  ff.,  monetary  experts  in  276- 

1.  The  plans  for  translation  were  upset  by  the  Second  World  War.  In  America  the 
book  is  evidently  being  circulated  on  microfilm,  being  unobtainable  in  any  other  form. 
(Only  a  handful  of  copies  for  review  reached  the  United  States  before  the  war  shut  off 
the  supply.— Translator.) 

2.  My  book  on  money  will  contain  more  on  this  subject.  (Because  of  the  premature 
death  of  the  author  this  book  has  never  appeared— However,  a  lengthy  article,  "  Theorie 
der  Wahrung,"  appeared  posthumously  in  the  Weltwirtschaftliches  Archiv,  Vol.  LXII 
(1949) .  35-88.-W.  F.  S.) 


F  re  face  Lo  Second  Edition  ''^" 

304  and  317-324;  price  control  officials  263,  333,  and  452-507;  geog- 
raphers and  statisticians  in  365-507;  sociologists  in  66-91  and 
223-262;  and  transportation  specialists  in  pages  127,  170-191  and 
440-444.  Students  may  skip  Part  I,  and  at  first  the  mathematics  as 
well.  Those  interested  in  town  and  regional  planning  will  consider 
especially  pages  329-357  and  440-444,  Part  IV  in  general  and,  finally, 
the  basic  material  in  Parts  I  and  II,  which  is  not  alway  easy.  Here 
they  will  find  what  economics  has  to  offer  today  about  the  spatial 
aspects  of  the  economy. 

In  addition,  of  course,  the  utilization  of  many  ideas  for  practical 
planning  needs  to  be  further  developed.  The  commission  to  prepare 
this  work  I  owe  to  the  friendly  interest  of  the  Secretary  of  State 
Dr.  Muhs,  Director  of  the  Reichsstelle  fiir  Raumordnung.  In  this 
connection  I  recall  with  pleasure  my  conversations  with  his  colla- 
borators, Ministerialdirigent  Dr.  Teubert,  First  Baurat  Koster,  Dr. 
Puttkammer,  and  Diplomvolkswirt  Wiesener.  But  above  all  I  am 
indebted  for  much  to  my  compatriot,  Oberregierungsrat  Dr.  Isen- 
berg,  a  pioneer  in  regional  research.  Then,  too,  the  contribution 
of  those  who  helped  to  make  the  book  technically  possible  is  not  to 
be  underestimated  today.  As  for  the  rest,  the  thanks  expressed  in 
the  first  edition  as  well  as  its  dedication  still  apply. 

When  the  first  edition  was  written  I  lacked  the  money,  and  now 
I  lack  the  time,  to  carry  my  plans  to  completion.  Most  of  my  powers 
were  then  consumed,  instead  of  in  actual  work,  in  merely  making 
this  possible.  For  generous  though  the  help  intended  for  science 
may  often  be,  little  of  it  reaches  the  garret  rooms  where  truth  is 
sought.  But  in  the  meantime  I  was  able  to  test  the  new  views  on 
many  theoretical  or  pressing  practical  problems.  Whether  these 
concerned  wide  areas  (Grossraum)  and  the  drawing  of  boundaries, 
the  establishment  of  towns  and  new  settlements,  or  such  apparently 
remote  subjects  as  currency,  foreign  trade,  the  formation  of  prices, 
and  market  forms,  they  have  proved  fruitful  throughout.  A  new 
economics  is  coming  into  existence.  But  not  enough  time  remains 
to  make  it  secure  in  peace  on  all  sides,  and  since  I  do  not  wish  to 
offer  what  may  be  attractive  at  the  moment  but  would  not  stand  a 
rigid  test  I  have  given  up  the  publication  of  most  of  my  results, 
even  though  I  could  use  some  of  them  in  my  memoranda.  It  is  not 
easy  to  stand  before  this  rich  harvest  with  hands  tied  if  one  has  with- 
in his  grasp  a  new  method  for  practicing  and  analyzing  economics. 

August  I.osch 
Kiel 

Autumn,  1943 


Contents 


Translator's  Note  v 

August  Losch  in  Memoriam,  by  Wolfgang  Stolper  vii 

Preface  to  the  First  Edition  xiii 

Preface  to  the  Second  Edition  xvi 

List  of  Figures  xxiii 

List  of  Tables  xxvii 

I.    Location  1 

A.  Systematic  Presentation  of  the  Location 

Problem  3 

1.  The  Meaning  of  the  Location  Problem  4 

2.  Specific  Locations  5 

a.  Effects  of  Locations  upon  One  Another  5 

b.  The  Relative  Position  of  Locations  9 

3.  Areal  Boundaries  13 

a.  Boundaries  between  Simple  Areas  13 

b.  Boundaries  between  Areal  Systems  13 

B.  Selected  Problems  of  Location  15 

4.  Industrial  Location  Theory  16 

a.  The  General  Principle  16 

b.  Practical  Execution  17 

5.  The  Theory  of  Agricultural  Location  36 

a.  Partial    (One-sided)    Orientation  36 

b.  Comprehensive  Solution  60 

c.  Agricultural  and  Industrial  Location 
Theory:  A  Comparison  63 

6.  Site  and  Reasons  for  Town  Settlement  68 

a.  Reasons  for  Town  Settlement  68 

b.  The  Site  of  Town  Formation  80 

7.  Site  and  Cause  of  Belt  Formation  85 

a.  Belts  of  Locations  Producing  Identical 
Goods  85 

b.  Belts  of  Different  Locations  90 

8.  The  Problem  of  General  Location  Patterns  92 


The  Economics  of  Location 

a.  The  Equilibrium  of  Locations  94 

b.  The  Separation  of  Locations  98 

c.  Conclusion  99 

II.    Economic  Regions  101 

A.  Economic  Regions  under  Simple  Conditions  105 

9.    The  Market  Area  105 

10.  The  Network  of  Markets  109 

a.  Continuous    Distribution    of    Popula- 

tion 109 

b.  Discontinuous  Distribution  of  Popula- 

tion 114 

c.  Regional  Networks  122 

11.  The  System  of  Networks  124 

a.  The  General  Pattern  124 

b.  Special  Cases  130 

12.  The  Network  of  Systems  135 

a.  The  Relation  of  Landscapes  to  One 

Another  135 

b.  The  Boundary  Region  136 

c.  Results  137 

B.  Economic  Regions  under  Difficult  Conditions  138 

13.  Some  New  Factors  139 

a.  Economic  Differences  139 

b.  Natural  Differences  178 

c.  Human  Differences  191 

d.  Political  Differences  196 

14.  Further  Restriction  of  Market  Areas  211 

15.  Economic  Regions  in  Reality  215 

a.  Spatial  Arrangement  215 

b.  On  a  Chaotic  Interpretation  219 

III.    Trade  223 

A     Description  of  Equilibrium  223 

16.  Six  Cardinal  Problems  of  the  Division  of 

Labor  and  Their  Interrelations  223 

17.  The  Six  Cardinal  Problems  of  the  Divi- 

sion  of  Labor  Discussed   Individually  226 

a.  The  Occupation  of  a  Person  226 

b.  The  Personnel  of  an  Industry  236 


Contents 


c.  The  Locality  of  a  Person  240 

d.  The  Occupants  of  a  Locality  245 

e.  The  Industry  in  a  Locality  248 

f.  The  Locality  of  an  Industry  255 

g.  Conclusion  262 

18.  Price  Gradients  263 
B.    Disturbance  of  the  Equilibrium  264 

19.  Self-Regulation  265 

a.  Transfer  of  Products   During  Short- 

run    Disturbances     (The    Transfer 

Problem)  265 

b.  Redistribution  of  the  Factors  of  Pro- 

duction with  Long-run  Disturbances 

(The  Combination  Problem)  305 

c.  What  Remains  of  the  Classical  Theory?  312 

20.  Regulation  from  Without  315 

a.  Regulation  of  the  Transfer  of  Prod- 

ucts   (The  Transfer  Problem)  316 

b.  Regulation    of    the    Distribution    of 

Factors  of  Production    (The  Com- 
bination Problem)  324 

c.  The    Practical    Value    of    Economic 

Theory  357 

IV.    Examples  361 

A.  Location  365 

21.  Locations  of  Production  365 

a.  Uniform  Distribution  365 

b.  Uneven  Distribution  376 

c.  National    Boundaries    as    Factors    in 

Location  382 

22.  The  Location  of  Towns  389 

B.  Economic  Areas  395 

23.  Simple  Market  Areas  395 

a.  The  Significance  of  Distance  for  the 

Individual  Enterprise  396 

b.  Description  of  Market  Areas  402 

c.  The  Economic  Importance  of  Distance  427 

24.  Regional  Systems  431 
a.    Number,  Spacing,  and  Size  of  Towns  431 


xxii  The  Economics  of  Location 

b.  Spatial  Arrangement  of  Towns  438 

c.  The  Function  of  Towns  439 

d.  Town  Plans  440 

25.  Frontier  Regions  445 
C.    Trade  452 

26.  Price  Levels  in  Space  452 

a.  Prices  of  Factors  of  Production  452 

b.  Product  Prices  476 

c.  Cost  of  Living  490 

27.  Price  Changes  in  Space  496 

a.  Spatial  Differences  in  the  Movement" 

of  Commodity  Prices  496 

b.  Spatial  Differences  in  the  Movement 

of  Interest  505 

Epilogue.    On  Space  508 

Subject  Index  509 

Name  Index  517 


List  of  Figures 

1.  The  concentration  of  locations  11 

2.  The  construction  of  isodapanes  19 

3.  Consumption  and  production  as  functions  of  distance  37 

4.  Effect  of  increased  freight  on  the  demand  for  a  cheap 

and  for  an  expensive  product  45 

5.  Rent  per  acre  as  a  function  of  distance  49 

6.  Intersection  of  two  profitability  planes  50 

7.  Thiinen  case  53 

8.  Inversion  of  the  Thiinen  rings  53 

9.  Contradiction  between  figures  8a  and  8e  55 

10.  Comparison  of  rent  per  hectare  of  Thiinen  case  and  in 

its  inversion  55 

11.  Potato  market  56 

12.  Corn  market  56 

13.  Rent  per  hectare  during  transition  56 

14.  Illustration  of  case  18  of  the  complete  system  58 

15.  Mixed  cropping  and  rings  58 

16.  Size  of  the  producing  unit  in  a)   industry  and  b)   agri- 

culture 64 

17.  Supply  of  the  same  market  by  several  entrepreneurs  70 

18.  Suitability  of  different  soils  for  different  products  86 

19.  Location  of  crops  as  a  function  of  soil  quality  and 

distance  88 
20-22.  Derivation  of  the  demand  cone  and  the  market 
area  from  the  demand  curve  for  the  product  as  func- 
tion of  distance  and  the  cost  curves  106 
23.  Development  of  market  areas  from  the  large  circle  to 

the  final  small  hexagon  110 

24-26.  The  three  smallest  market  areas  U7 

27.  The  ten  smallest  economic  areas  118 

28.  Theoretical  pattern  of  an  economic  landscape  125 

29.  Theoretical  pattern  of  an  economic  landscape,   but 

without  nets  125 

30.  Indianapolis  and  environs  125 


i[xiv  The  Economics  of  Location 

31.  Toledo  and  environs  125 

32.  The  transport  lines  in  the  ideal  economic  landscape  127 

33.  Location  of  regional  centers  in  the  complete  system  128 

34.  Regions  with  equal  structure,  k  =  3  128 

35.  Regions  with  equal  structure,  k  =  4  132 

36.  Regions  with  equal  structure,  k  =  7  1 32 

37.  Part  of  a  square  economic  landscape  134 
38-39.  Location  of  landscapes  in  respect  to  one  another  135 

40.  Comparison  of  individual  demand  with  respect  to  the 

c.  i.  f.  and  f.  o.  b.  price  140 

41.  Various  types  of  total  demand  curves  145 

42.  Factory  price  and  distance  149 

43.  Three  individual  demand  curves  with  respect  to  f .  o.  b. 

price   as   function  of  distance,   corresponding   total 

revenue  curves,  and  corresponding  transport  cones  151 

44.  Geometric  solution  of  limits  of  price  differentiation  154 

45.  Comparison   of  price   discrimination,   uniform   f.  o.b. 

price,  and  uniform  c.  i.  f.  price  161 

46.  Price  cones  of  agricultural  products  around  towns  167 

47.  Similarity  of  price  differentiation  for  goods  and  spatial 

freight  differentiation  through  zonal   tariffs  172 

48.  Effect  of  new  large-scale  economies  on  size  of  market 

area  176 

49.  Comparison   of  market   area   in    thickly   settled   and 

thinly  settled  regions,  with  equal  cost  curves  181 

50.  The  law  of  refraction  184 
50.  Schematic  representation  of  efficient  route  from  Hawaii 

to   New   Orleans   via   Panama   Canal   and   possible 

Nicaragua  cut  186 

52.  Effect  of  gate  cities  on  market  and  supply  areas  190 

53.  Economic  and  political  borders  204 

54.  Schematic  representation  of  the  six  basic  questions  of 

the  division  of  labor  224 

55.  Population  density  of  northeastern  Europe,   1930  258 

56.  Effects  of  a  price  inflation  on  market  areas  268 

57.  The  spread  of  price  changes  271 

58.  World-wide  price  waves  304 

59.  Possible  effect  of  customs  union  on  demand  and  price  341 

60.  Reduction  of  market  areas  by  a  tariff  341 


List  of  Figures  xxv 

61.  Member    banks    o£    the    Federal    Reserve    Bank    of 

Chicago  in  Iowa,  January  1,  1926  366 

62.  Bank  locations  in  the  nine  northwest  counties  of  Iowa, 

1926  366 

63.  Principal  European  fairs^  1921  367 

64.  Agricultural    population   per   square   mile   in   North 

America    (United  States,  1930;  Canada,  1931)  375 

65.  Rotation  of  crops  as  a  function  of  distance  from  a 

village  382 

66.  Distribution  of  towns  in  Iowa,  1930  389 

67.  Distribution  of  towns  in  England,  1910  389 

68.  Increase  in  distance  between  towns  west  of  Chicago  390 

69.  Parceling  of  fields  on  a  farm  in  the  Administrative 

District  of  Herrenberg  400 

70.  Size  of  wholesale  market  areas  by  goods,  1929  404 

71.  Encirclement  of  a  small  town  by  a  large  town  411 

72.  Market  area  of  a  house  in  Kansas  City  for  fine  woolen 

clothing  and  overalls  and  work  clothes  413 

73.  Market  areas  of  five  hardware  trade  centers  415 

74.  Method  of  determining  retail  market  areas  418 

75.  Sales  area  for  building  lumber  and  cement,   Cedar 

County,  Iowa  418 

76.  Supply  and  market  areas  for  Muscatine,  Iowa  419 

77.  Hierarchy  of  supply  areas  for  tung  oil  420 
78-79.  The  great  world  wheat  markets,  1928-29  421 

80.  England  as  a  corner  market  at  the  center  of  world 

trade  routes,  1936  425 

81.  Distance  and  foreign  trade  429 

82.  Shape  and  street  network  of  a  small  town  442 

83.  The  French  hinterland  of  Geneva  445 

84.  Influence  of  the  drawing  of  the  boundary  upon  the 

market  area  of  Bischofswerder,  East  Prussia  446 

85.  The  network  of  railways  on  the  American-Canadian 

border  447 

86.  The  financial  sphere  of  influence  of  El  Paso,  1914  448 

87.  Price  of  land  in  Nordhorn,  1926-29  453 

88.  Value  of  agricultural  units  around  Stuttgart  and  Heil- 

bronn,  1935  454 

89.  Gradation  of  wages  in  the  German  Empire,  1941  457 


jcxvi  The  Economics  of  Location 

90.  The  Stuttgart  commuting  area  457 

91.  Monthly  wage,  without  board,  of  agricultural  workers, 

United  States,  1933  458 

92.  Price  in  dollars  for  resoling  and  heeling  a  pair  of  shoes, 

United  States,  1936  459 

93.  Price  in  cents  for  laundering  a  man's  shirt.  United 

States,  1936  459 

94.  Increase  in  the  rate  of  interest  with  distance  from  New 

York,  1919-25  462 

95.  Increase  in   the  rate  of  interest  with  distance  from 

Houston,  Texas,  1936  465 

96.  Spatial  pattern  of  wheat  prices  in  the  United  States, 

1910-14  478 

97.  Producer  prices  for  potatoes.  United  States,  1906-15  480 

98.  Retail  prices  of  potatoes,  United  States,  1936  480 

99.  Isotimes  for  soap.  United  States  and  Canada,  1936  488 

100.  Westward  movement  of  the  depression  in  Iowa,  1929- 

31  497 

101.  Comparison  of  house  rents  in  the  United  States  and 

Canada,  1929-37  500 

102.  The  ratio  of  price  levels  in  the  North  and  South  in 

the  United  States  and  its  dependence  upon   tariff 
policy,  1820-1935  502 


List  of  Tables 


1.  Classification  of  locations  34 

2.  Complete  system  of  spatial  order  in  agriculture  for  two 

crops  39 

3.  Symbols  of  spatial  arrangement  95 

4.  System  of  equations  I  97 

5.  Demand  as  a  function  of  regional  shape  1 1 1 

6.  The  ten  smallest  possible  market  areas  119 

7.  Calculation  of  n  119 

8.  Regions  with  homogeneous  structure  131 

9.  International  trade  227 

10.  Interpersonal  trade  228 

11.  Comparative  efficiencies    (comparative  advantages)    of 

the  countries  229 

12.  Order  of  comparative  advantages  231 
13-14.  Example  of  determination  of  the  price  of  land  255 

15.  Transfer  and  construction  of  currency  282 

16.  Transfer  with  different  reserve  ratios  283 

17.  System  of  methods  for  regional  planning  347 

18.  Significance  of  regional  production  in  the  United  States, 

1929  368 

19.  Surplus,  self-sufficient  and  deficit  regions  369 

20.  Employment  per  1,000  inhabitants.  East  Prussia,  Wurt- 

temberg,  Ruhr,  Reich  373 

21.  Frequency  distribution  of  towns  in  Iowa,  1930,  by  size 

and  distance  391 

22.  Distances    separating    towns    in    various    parts    of    the 

United  States  392 

23.  Distances  separating  English  towns,  1910  394 

24.  Selling  cost  and  distance  398 

25.  Relation  of  sales  radius   to  cost  in  certain  wholesale 

trades  399 

26.  Size  of  market  areas  for  wholesale  trade  in  the  United 

States  according  to  goods,  1929  405 

27.  Size  of  wholesale  market  areas  by  cities,  1929  407 

28.  Distance   and   size  of  demand   in   wholesale   trade,   by 

counties  409 


xxviii  ^^^  Economics  of  Location 

29.  Distance  and  size  of  demand  in  retail  trade  for  similar 

places  in  three  counties  in  Iowa  410 

30.  Distance  and  size  of  demand  412 

31.  Source  of  wheat  imports,  by  importing  country  and 

exporting  country,  1928-29  423 

32.  Germany's  share  in  the  foreign  trade  of  European  coun- 

tries, 1928  430 

33.  Structure  of  region,  with  k  ==  3  431 

34.  Regional  systems  in  Iowa,  theory  and  reality  435 

35.  Increase  in  interest  rate  on  bank  loans  with  distance  in 

Texas,  1936  465 

36.  Increase  in  interest  rate  on  bank  deposits  with  distance, 

Texas,  1936  466 

37.  Orange  prices  and  distance  481 

38.  Local  differences  in  nonagricultural  retail  prices  in  the 

United  States  and  Canada,  1936  487 

39.  Comparison   of   price    movements    on    the    American- 

Canadian  border,  1915-37  499 

40.  National  price  increase  after  devaluation   in  Canada 

and  the  United  States  500 

UNNUMBERED    TABLES 

One-to-one  correspondence  between  international  and 
interpersonal  trade  235 

Relation  of  physical  yield  of  various  crops  to  the 
proportion  of  total  production  of  the  United  States 
by  New  England,  Middle  Atlantic,  and  East  North 
Central  States  376n. 

Selling  cost  dependent  on  distance  as  percentage  of 
total  cost.  United  States  397 

Freight  per  ton-mile  relative  to  factory  price,  Germany     397n. 

Theoretical  and  actual  number  of  places  in  Christaller 
system  432 

Expenses  of  national  banks  as  percentage  of  deposits, 
1935  470 

Spread  of  interest  rates  between  New  York  and  twenty- 
seven  financial  centers  in  the  South  and  West,  1923-35     505 


PART   ONE.      LOCATION 


OUR  EXISTENCE  in  time  is  determined  for  us,  but  we  are 
largely  free  to  select  our  location.  This  is  influenced,  though 
not  dictated,  by  our  place  of  origin.  Finding  the  right  location 
is  essential  to  successful  life,  but  it  is  essential  also  to  a  successful 
enterprise,  to  the  establishment  of  a  lasting  settlement— in  short,  to 
group  survival.  In  addition,  a  suitable  location  must  be  a  location 
for  the  right  events.  On  closer  examination,  these  originally  simple 
problems  constantly  divide  and  subdivide  anew.  Thus  presentation, 
unlike  investigation,  must  begin  by  introducing  some  order  into 
this  rapidly  confusing  abundance  of  problems. 


A.  Systematic  Presentation  of 
the  Location  Problem  ^ 

No  MAN-MADE  SYSTEM  can  avoid  the  arbitrary.  None  is  conclusive 
for  we  do  not  know  the  final  cause  of  things.  We  know  only  a 
mutual  relationship,  not  a  simple  series  of  causes  from  beginning 
to  end,  from  above  to  below.  It  is  basically  immaterial  where  our 
presentation  begins,  since  we  cannot  linger  over  the  parts  without 
considering  the  whole.  If  a  system  is  regarded  as  an  order  of 
preference,  the  emphasis  lies  heavily  on  the  word  order.  We  order 
our  facts  according  to  viewpoints  that  are  important  to  us.  Hence 
the  same  thing  appears  again  and  again  but  is  seen  differently, 
whereas  in  a  proper  sequence,  in  an  ideal  system,  it  would  have  a 
unique  place.  Just  as  the  first  three  parts  of  this  book  imply  no 
clear-cut  separation,  so  classification  within  this  as  within  all  other 
sections  is  only  a  matter  of  convenience.  This  is  already  shown  by 
the  fact  that  not  until  the  third  part  does  the  argument  expand  into 
a  comprehensive  view  of  economics  in  space  and  the  division  of 
labor  in  general.  Here  we  limit  ourselves  to  the  narrower  problem 
that  forms  the  subject  of  traditional  location  theory,  namely,  where 
a  particular  economic  activity  is  to  be  found.  In  judging  the  mani- 
fold contributions  to  this  theme  it  is  helpful  to  fix  their  place  in 
the  theory.  Moreover,  only  thus  can  we  recognize  the  basic  problems. 

1.  This  concise  review  presupposes  in  its  details  some  familiarity  with  the  subject. 
Hence  the  beginner  should  merely  glance  at  first  over  pp.  5-14. 


Chapter  1.     The  Meaning  of  the  Location  Problem 


The  question  of  actual  location  must  be  distinguished  from  that 
of  the  rational  location.  The  two  need  not  coincide.  Interest  in 
the  first  is  divided  between  identifying  and  explaining  a  site,  and 
may  concern  itself  either  with  an  individual  case  and  thus  be  essen- 
tially historical  in  character,  or  with  a  behavior  that  is  typical  at 
least  for  an  epoch.  From  this  follow  rules  for  the  considerations 
by  which  entrepreneurs  let  themselves  be  guided  in  choosing  an 
actual  location.  It  is  often  important  to  know  this.  But  it  would 
be  dangerous  to  conclude  that  what  is  must  also  be  rational  since 
otherwise  it  could  not  exist,  and  that  any  theoretical  determination 
of  the  correct  location  would  therefore  be  superfluous.  Such  a 
capitulation  to  reality  is  as  useful  as  the  advice  of  those  who  on 
principle  contradict  no  one:  a  contemptible  attitude  that  is  satisfied 
to  accept  one's  era  instead  of  serving  it.  Of  what  value  is  a  science 
that  does  not  observe  Schiller's  valiant  watchword:  "  Live  with  thy 
century,  but  be  not  its  creature;  give  to  thy  contemporaries,  but 
give  what  they  need,  not  what  they  laud  "?  ^  No!  The  real  duty  of 
the  economist  is  not  to  explain  our  sorry  reality,  but  to  improve  it. 
The  question  of  the  best  location  is  far  more  dignified  than  deter- 
mination of  the  actual  one. 


1.  Ueber  die  asthetische  Erziehung  des  Menschen,  9.  Brief. 


Chapter  2.     Specific  Locations 


a.     EFFECT    OF   LOCATIONS    UPON    ONE    ANOTHER 

The  PRINCIPLES  for  a  rational  choice  of  location  vary  according  to 
whether  we  view  them  (as  entrepreneurs)  from  the  standpoint  of 
the  individual,  or  (as  regional  planners)  from  the  standpoint  of 
the  whole.  According  to  the  point  of  view  we  perceive  only  one 
factor  determining  location,  or  two. 

§1.    Theory  of  Location  for  an   Individual  Firm 

a.    Choice  of  Location  for  the  Economic  Unit 

The  problem  is:  Given  all  locations  but  one,  to  determine  this.^ 
The  individual  solves  this  problem  according  to  his  best  advantage. 
(This  is  the  first  general  tendency.)  As  a  rule,  he  must  find  the 
most  favorable  center  of  a  production,  sales,  or  supply  area.  The 
first  two  cases  concern  the  location  of  a  producer,  the  third  that 
of  a  consumer. 

1.  Location  for  a  Producer.  The  situation  of  available  means 
of  production,  of  competition,  and  of  consumption  must  be  known 
as  geographical  data,  but  the  significance  of  these  factors  is  variable 
in  the  extreme.  For  the  location  of  a  farm  it  is  highly  important 
that  its  production  be  areal,  whereas  its  market  may  be  thought  of 
as  punctiform.  For  a  typical  nonfarm  enterprise  the  situation  is 
reversed,  and  the  theory  of  agricultural  location  differs  therefore 
from  that  of  industrial  location.  The  latter  has  been  discussed 
especially  by  Weber  though  in  very  simple  terms,  to  be  sure;  the 
former,  by  J.  H.  von  Thiinen.^ 

2.  Location  of  a  Consumer.  His  location  depends  upon  the 
location  of  the  producers  and  of  neighboring  centers  of  consump- 

1.  The  pricing  problem  of  an  individual  enterprise  is  no  different.  As  in  any  one 
individual  case  price  can  be  explained  by  costs,  so  any  one  location  can  be  explained 
by  others.  The  general  theory  of  pricing  must  not,  of  course,  follow  this  circular 
reasoning,  and  neither  must  the  general  theory  of  location.  In  either  case  only  a 
system  of  simultaneous  equations  can  properly  demonstrate  the  interdependence. 

2.  J.  H.  von  Thiinen,  Der  Isolierte  Staat  in  Beziehung  auf  Landwirtschaft  und 
Nationalokonomie   (Hamburg,  1826),  §11  and  elsewhere. 


6  Part  One.    Location 

tion.  This  case  was  especially  important  in  the  Middle  Ages:  An 
inland  town  would  develop  only  where  the  neighboring  towns 
left  it  an  adequate  source  of  agricultural  supplies.  The  situation 
is  fundamentally  similar  today  for  cotton  mills,  flour  mills,  slaughter 
houses,  and  so  on.  Some  discussion  of  this  subject  is  to  be  found  in 
the  literature  on  economic  history  (Sombart) ,  though  as  far  as  I  am 
aware  its  theory  has  not  been  so  thoroughly  worked  out  as  that  of 
the  first  case. 

fi.    Repercussions  of  Individual  Choices  of  Location 

In  adopting  the  viewpoint  of  the  individual  economic  unit  we 
appear  to  have  freed  ourselves  from  the  general  interdependence  of 
locations,  and  thus  to  be  able  to  give  a  more  exact  solution  than 
that  contained  in  the  general  equations  of  location  to  be  discussed 
below.  But  certain  repercussions  immediately  appear,  which  radiate 
from  the  desired  location  back  to  those  that  determine  it.  As  long 
as  we  consider  only  the  first  and  nearest  of  the  determining  locations 
(as  in  what  follows)  we  still  deal  with  a  problem  of  partial  equi- 
librium. But  as  soon  as  we  endeavor  to  take  account  of  all  inter- 
actions we  are  faced  with  general  interdependence   (as  in  §2) . 

1.  Influence  on  Competitors.  When  the  new  enterprise  has 
chosen  its  location  competitors  may  re-examine  theirs.  This  difficult 
problem  was  first  suggested  by  H.  Hotelling,^  but  treated  on  such 
simplified  assumptions  that  his  conclusion  (a  tendency  to  agglomera- 
tion) cannot  be  generalized.  Under  uniform  conditions  in  a  free 
market  the  individual  has  no  latitude  in  the  choice  of  his  location. 
The  problem  can  thus  have  practical  importance  only  either  during 
the  transition  to  equilibrium  or,  in  equilibirium  itself,  only  in 
those  industries  where  human  or  natural  differences  play  a  role  or 
where  a  single  enterprise  produces  a  large  part  of  total  output. 
After  production  has  been  divided  among  individual  firms,  a  residue 
may  remain  in  this  case  that  is  too  small  to  permit  the  existence  of 
an  additional  firm,  yet  large  enough  to  allow  those  already  estab- 
lished to  operate  well  to  the  right  of  Chamberlin's  point.*  These 
enterprises  then  have  some  latitude  of  choice,  and  may  fight  among 
themselves  for  the  most  advantageous  location. 

2.  Influence  on  Customers  and  Suppliers.  We  can  distinguish 
effects  on  the  form  and  the  substance  of  their  activities. 

(aa)     Effects  on  Form.    First,  the  form  of  consumption  as  a 

3.  Harold  Hotelling,  "  Stability  in  Competition,"  Economic  Journal,  1929,  pp.  41-57. 

4.  See  below,  p.  109,  note  1. 


specific  Locations  7 

function  of  distance.  Given  the  location  of  its  production,  the 
consumption  of  a  particular  product  may  assume  different  forms, 
depending  on  the  distance  from  the  site  of  its  manufacture.  For 
example,  it  might  prove  advantageous  to  ship  a  large  machine 
already  assembled  to  a  near-by  purchaser.  The  additional  cost  of 
shipping  a  bulky  machine  rather  than  its  parts  will  be  more  than 
offset,  up  to  a  certain  distance  from  the  factory,  by  savings  in  the 
cost  of  mounting.  Beyond  this  critical  distance,  on  the  other  hand, 
the  machine  will  be  shipped  knocked  down.^ 

Second,  the  form  of  production  as  a  function  of  distance.  Given 
the  place  of  consumption  of  a  product,  the  particular  form  in  which 
it  is  produced  may  vary  with  the  distance  from  that  place.  By  form 
of  production  may  be  meant  intensiveness,  that  is,  the  method  of 
cultivation  (Thiinen) ;  or  the  stage  to  which  factory  production 
is  carried  out  locally.  If  local  finishing  is  more  expensive  than 
centralized  finishing,  perhaps  because  the  advantages  of  large-scale 
production  cannot  be  utilized  so  fully,  but  freight  per  unit  of 
consumption  is  less  when  a  product  is  shipped  in  finished  rather 
than  crude  condition,  then  it  may  pay  at  a  certain  distance  from 
the  consumer  to  ship  frozen  meat,  say,  instead  of  livestock  for 
slaughter.  In  these  cases  the  final  product  always  remains  the  same. 
From  this  we  must  distinguish  the  cases  in  which  different  end 
products  such  as  fresh  milk,  cream,  or  butter  are  prepared  from  the 
same  original  products,  depending  on  the  distance  from  the  con- 
sumer. We  then  deal  no  longer  with  different  competing  forms, 
but  with  different  products— the  subject  of  the  next  section. 

(bb)  Influences  on  the  Substance  of  Economic  Activity.  First, 
the  object  of  consumption  as  a  function  of  distance.  Suppose  com- 
peting goods  are  produced  in  the  same  place.  Where  each  will  be 
consumed  may  depend  on  the  distance  from  their  origin.^  Consider, 
for  example,  rich  and  poor  ores,  both  mined  at  the  same  spot,  the 
former  below,  the  later  at  the  surface.  Since  the  cheap  ore  is  there- 
fore cheaper  per  consumption  unit,  though  more  expensive  to  ship, 
it  has  an  advantage  in  the  neighborhod  of  the  mine,  while  the  rich 
ore  is  purchased  only  by  more  distant  iron  works. 

Second,  the  object  of  production  as  a  function  of  distance.  We 
come  to  the  other  half  of  Thiinen's  famous  statement  of  the  prob- 
lem, the  first  half  of  which  concerned  the  form  of  production  as  a 
function  of  distance  from  the  market.  Suppose  the  locations  for  the 

5.  See  below,  p.  37. 

6.  See  W.  Launhardt,  Mathemaiische  Begriindung  der  Volkswirtschaftslehre    (Leip- 
zig, 1885)  ,  p.  164. 


8  Part  One.     Location 

consumption  of  various  products  to  coincide  in  a  town.  These  prod- 
ucts compete  for  land  for  their  cultivation.  Thiinen  has  shown 
that  under  certain  conditions  their  cultivation  is  arranged  in  rings 
around  the  market.    We  shall  return  to  this  problem  laterJ 

§2.  The  General  Theory  of  Location 

a.    General  Equations  of  Location 

If  we  wish  to  be  precise  and  to  consider  the  influence  of  the 
selection  of  a  particular  location  on  all  other  locations— in  the 
example  of  Thiinen  just  mentioned,  for  instance,  the  repercussions 
of  the  location  of  our  town  not  only  on  the  particular  farms  that 
supply  it,  but  on  all  agriculture  and  on  all  other  towns— then  we 
enter  upon  the  general  theory  of  location.  The  repercussions,  strictly 
speaking,  are  transformed  into  mutual  relations,  and  it  ceases  to  be 
meaningful  to  pick  out  one  location  and  examine  its  relation  to  its 
neighbors  in  isolation.  We  are  faced  with  the  interdependence  of 
all  locations.  Equilibrium  of  the  location  system  can  therefore  no 
longer  be  charted,  but  can  be  represented  only  by  a  system  of  equa- 
tions that  are  insoluble  in  practice.  The  conditions  that  they  express, 
rather  than  the  equations  themselves,  are  of  great  interest  indeed. 
For  they  contain  the  conditions  for  the  functioning  of  the  whole 
system  and  are  therefore  more  important  than  all  that  the  special 
location  theory  has  to  offer  in  the  way  of  realistic  details.  With  the 
general  equations  we  encounter  the  other  basic  force  that  deter- 
mined location:  the  tendency  to  equalization  of  the  advantages  of 
the  individual  economic  units  and  (in  a  market  into  which  entry 
is  possible)   the  maximization  of  the  number  of  competitors.^ 

j8.    The  Simplifying  Theory  of  Economic  Regions 

Between  the  theory  of  individual  locations  and  that  of  location 
patterns  stands  the  theory  of  economic  regions.  It  shares  with  the 
former  the  advantage  of  geometric  representation,  with  the  latter 
a  breadth  of  subject.    It  shows  the  universal  interdependence  of 

7.  An  industrial  parallel  appears  when  different  goods  are  made  from  the  same 
raw  material  with  different  weight  losses.  See  O.  Englander,  Theorie  des  Giiterver- 
kehrs  und  der  Frachtsdtze   (Jena,  1924),  pp.  129  f. 

8.  As  the  latter  eliminates  profits  (though  absence  of  profits,  on  the  other  hand, 
does  not  assure  maximization  of  the  number  of  independent  economic  existences) 
one  may  speak  roughly  of  a  tendency  toward  equalization  and  elimination  of  profits; 
i.  e.,  of  an  equalization  of  incomes  among  independents  and  between  them  and 
dependents.  Later  we  shall  assume  free  entry  to  markets  as  a  more  desirable  situation, 
and  thus  treat  both  tendencies  together. 


specific  Locations  9 

locations  with  such  simplifications  that  it  can  be  charted.  It  neglects 
in  particular  natural  inequalities  and  in  some  though  not  all  respects 
urban  demand.  It  considers  the  relations  between  all  producers  and 
consumers  of  the  same  goods,  and  between  the  producers  of  different 
goods  at  least  in  so  far  as  they  are  significant  for  the  establishment  of 
major  cities  and  main  transport  arteries.  If  the  suppressed  factors 
are  introduced  it  is  quite  probable  that  the  picture  would  be  some- 
what changed,  but  it  is  unlikely  that  it  will  be  wholly  invalidated. 
Because  of  their  importance,  a  separate  part  of  this  book  will  be 
devoted  to  economic  regions. 

b.     THE    RELATIVE    POSITION    OF    LOCATIONS 

§1.     The  Basic  Types 

We  shall  now  discuss  the  results  of  a  rational  choice  of  location. 
Definite  and  characteristic  combinations  emerge  between  the  places 
where  a  commodity  is  produced  and  those  where  it  is  consumed, 
depending  on  their  numbers  and  locations.  In  the  market  as  a 
whole  there  may  well  be  a  hundred  such,  which  usually  will  split 
up  into  smaller  groups  of  which  the  majority  find  it  advantageous 
to  deal  principally  with  one  another,  or  exclusively  so  if  the  products 
of  the  individual  manufacturers  are  homogeneous.  Every  group  is  a 
submarket.  Those  submarkets  that  have  immediate  contact  with 
each  other,  as  well  as  those  markets  that  are  not  split  up  into 
further  subdivisions,  may  be  reduced  to  a  few  basic  types:  It  occurs 
only  rarely  that  a  single  producing  center  deals  with  a  single  con- 
suming center.  Yet  nonagricultural  location  theory  has  preferred 
to  base  itself  on  this  limiting  case.  As  a  rule,  several  producers  are 
grouped  about  one  consumer,  or  several  consumers  about  one 
producer.  We  speak  accordingly  of  regions  of  supply  or  of  demand, 
and  include  both  under  the  term  market  areas. 

These  two  basic  types  of  positional  relations  are  the  core  of 
every  determination  of  a  location,  areas  of  demand  playing  a  larger 
role  in  the  nonagricultural  theory  and  areas  of  supply  in  the  agri- 
cultural. The  latter  has  been  discussed  principally  by  Thiinen,  the 
former  by  Launhardt,  and  the  borderline  cases  by  Weber.  It 
makes  little  difference  whether  the  number  of  locations  distributed 
throughout  the  market  area  is  large,  as  in  agriculture,  or  small,  as 
it  often  is  with  nonagricultural  enterprises.  According  to  circum- 
stances we  deal  with  complete  or  with  incomplete  market  areas, 
but  fundamentally  the  situation  is  the  same.  Nor  is  it  altered  if  a 
center  of  production  included  many  independent  enterprises  in  the 


iQ  Part  One.     Location 

same  line  of  business,  each  of  which  supplies  the  entire  area.  In 
respect  to  their  common  area  of  demand  they  may  be  treated  as 
one  firm,  and  their  supply  curves  may  correspondingly  be  added.^ 
From  this  it  follows  that  the  nature  of  the  area  is  determined  not  by 
the  number  of  buyers  or  sellers,  but  by  the  number  and  position  of 
their  locations. ^°'"  The  locations  of  the  producers  and  consumers 
of  the  same  product,  as  well  as  of  different  products,  may  be  situated 
anywhere  or  may  be  agglomerated.  These  agglomerations  are  impor- 
tant enough  to  be  treated  as  a  special  problem. 

§2,     Agglomeration  of  Locations 

a.    Punctiform  Agglomeration 

The  questions  why  the  best  locations  for  many  producers  (or 
consumers)  sometimes  coincide,  why  production  in  some  places  is 
so  unusually  great,  and  why  and  where  towns  grow,  are  one  and 
the  same.  The  answer  must  distinguish  between  agglomeration  of 
locations  for  the  production  of  similar  commodities  and  that  for 
the  production  of  different  commodities.  As  to  the  former  category, 
we  set  aside  the  case  where  a  particular  place  has  only  a  single  large 
firm  that  has  merely  attracted  a  few  local  enterprises  to  the  spot. 
At  present  we  shall  discuss  how  several  similar  and  independent 
enterprises  can  exist  in  the  same  place  as  the  result  of  purely 
rational  considerations;  that  is,  if  either  mergers  or  migration  of 
some  firms  could  occur  without  friction.  In  large  cities,  finally,  the 
concentration  of  similar  and  different  enterprises  may  occur  together. 
The  relation  of  all  these  agglomerations  to  one  another  is  subject 
to  special  laws,  which  will  be  discussed  in  Part  II. 

p.    Areal  Agglomerations 

With  punctiform  agglomerations  the  individual  locations,  or  at 
least  their  centers,  coincide.  Areal  agglomerations  are  distinguished 
by  the  fact  that  the  locations  of  their  centers  lie  close  together 

9.  Otherwise  some  product  differentiation  would  have  to  exist. 

10.  If  numbers  alone  were  relevant— i.  e.,  if  locations  were  evenly  distributed— areas 
of  supply  would  result  if  in  the  economy  as  a  whole  the  number  of  production  centers 
exceeded  that  of  consumption  centers,  and  vice  versa  for  areas  of  demand. 

11.  The  nature  of  the  area  is  in  turn  an  essential  factor  determining  the  market 
form,  together  with  the  number  and  importance  of  buyers  and  sellers,  their  market 
behavior,  and  their  complementarity.  It  was  a  mistake  to  think  that  the  market  form— 
i.  e.,  the  method  and  results  of  price  formation— could  be  known  merely  from  the 
number  of  buyers  and  sellers  without  their  locational  pattern.  In  general,  the  tradi- 
tional market  forms  acquire  an  essentially  different  content  as  soon  as  they  are  seen 
geographically.    But  there  is  neither  time  nor  space  to  develop  this  here. 


specific  Locations  '^ 

without,  however,  coinciding.  This  has  the  important  consequence 
that  in  the  latter  case  the  market  areas  of  the  various  locations 
remain  separate  though  close  together,  whereas  in  the  former  they 
coincide  precisely  near  the  concentration  of  locations  but  in  turn 
may  be  of  wide  extent.  An  example  of  an  areal  agglomeration  of 
locations  is  the  network  of  the  supply  areas  of  cotton  gins  in  the 
United  States,  which  are  distributed  with  fair  regularity  throughout 
the  cotton  belt  and  are  also  restricted  to  it.  An  example  of  puncti- 
form  agglomeration  of  locations  is  the  factories  producing  men's 
collars,  practically  all  of  which  are  situated  in  Troy,  New  York,  but 


Areal 

1 

none 

Restricted 
market  network 

Cluster 

1 

Z 

3 

t 

^ 

^ 

^ 

• 

True  network 
(bakeries) 

Belt  (cotton  gins)   i 

District  (coal  mines) 

Place  (collars) 

Fig.  I.    The  Concentration  of  Locations 

whose  market  includes  the  whole  of  the  United  States.  There  is, 
however,  a  third,  intermediate,  form.  Most  of  the  American  coal 
mines  are  not  concentrated  at  one  site,  though  they  are  restricted 
to  a  relatively  small  territory.  Nevertheless  they  do  not  supply 
arbitrarily  those  areas  that  lack  coal.  The  importance  of  overlapping 
coal  shipments  is  somewhat  overestimated.  They  depend  partly  on 
quality  differences.^^  In  the  main  they  are  the  result  of  irrational 
freight  rates.  On  the  whole  it  may  be  said,  therefore,  that  each 
section  of  the  coal-producing  area  has   its  own   special   outlets." 


12.  Thus  the  steel  works  in  the  Chicago  area  get  their  coal  from  the  Pittsburgh 
region  because  the  coal  from  the  much  nearer  Illinois  fields  is  not  suitable  for  coking. 

13.  Even  with  small  districts  this  makes  good  sense:  it  prevents  crosshauls  within 
a  district  that  is  already  overburdened  with  traffic.  When  this  district  is  of  even  rela- 
tively small  extent  a  sensible  organization  of  the  markets  becomes  difficult.  Imagine 
a  circular  coal  deposit,  and  assume  the  demand  to  be  so  small  that  only  the  mines  at 
the  periphery  are  kept  busy.  Then  each  mine  will  supply  a  sharply  defined  sector  of 
the  surrounding  tenitory.  With  increasing  demand  it  will  pay  to  work  the  mines  in 
the  next  inner  ring.  Strictly  speaking,  therefore,  rather  than  the  entire  coal  field  only 
an  outer  ring  is  worked,  whose  width  varies  with  demand.  The  nearer  the  mines  are 
to  the  periphery  the  larger  is  the  rent  they  yield.  The  situation  would  be  simplest 
if  coal,  like  cotton,  say,  were  collected  at  a  few  cents  at  the  edge  of  the  circle  and  then 


12  Part  One.    Location 

Hence  in  areal  agglomeration  of  locations  for  the  same  industry  we 
must  distinguish  the  belt,  where  the  market  networks  are  compressed 
close  together;  and  the  district,  where  the  markets  are  separated, 
while  only  their  centers  are  compressed.  Figure  1  pictures  the  dif- 
ferences of  the  last  two  agglomerations  from  complete  dispersal  on 
the  one  hand  to  punctiform  concentration  on  the  other. 

Hitherto  we  have  been  discussing  only  the  case  of  a  single 
industry.  But  there  is  an  areal  as  well  as  a  punctiform  agglomeration 
of  locations  for  different  activities:  the  so-called  industrial  areas. 
In  their  structure  they  resemble  partly  belts  and  partly  districts. 


redistributed  from  tliese.  Producers'  and  consumers'  rents  would  vary  then  only  with 
their  distances  from  these  collecting  centers.  Their  supply  and  sales  areas  would  be 
easily  determined.  In  reality  the  situation  is  somewhat  more  complex,  but  it  is  not 
worth  while  to  go  into  the  details  here. 


Chapter  3.     Areal  Boundaries 


a.     BOUNDARIES    BETWEEN    SIMPLE    AREAS 

Besides  the  locations  themselves,  the  lines  that  separate  them  in 
areal  distribution  are  of  interest,  and,  in  punctiform  distribution, 
the  areas  of  influence.  We  must  therefore  distinguish  between 
(1)  boundaries  between  different  kinds  of  goods  (i.  e.,  areas  that 
produce  or  consume  different  kinds  of  goods) ,  and  (2)  boundaries 
between  different  kinds  of  markets  (i.  e.,  areas  that  sell  the  same 
product  in  different  markets,  or  buy  from  them) .  Thiinen's  rings 
are  an  example  of  the  first;  separation  of  the  sales  areas  for  two 
competing  enterprises  in  different  locations  is  an  example  of  the 
second.  We  may  also  call  the  latter  the  boundaries  of  competing 
locations,  the  former  the  boundaries  of  competing  goods. 

The  boundaries  separating  areas  of  competing  locations  delimit 
the  supply  and  demand  areas  of  identical  goods.  The  boundaries 
separating  areas  of  competing  goods  delimit  the  areas  of  production 
or  consumption  of  different  goods,  or  at  least  of  different  forms  of 
goods. 

The  latter  are  already  given  with  the  position  of  all  locations, 
but  the  former  must  be  calculated  from  the  locations.  With  homo- 
geneous goods  the  boundaries  are  sharp  if  buyers  and  sellers  are 
scattered  and  numerous,  and  if  the  center  of  each  area  is  treated 
as  though  the  other  centers  did  not  exist.  Otherwise  the  markets 
overlap  and  the  boundaries  become  indistinct. 

b.      BOUNDARIES    BETWEEN    AREAL    SYSTEMS 

There  are  systems  in  which  the  areas  for  different  goods  are 
separate  (as  in  the  Thiinen  case)  or  overlap  (as  in  economic 
provinces) .  Depending  on  the  system,  we  get  only  boundary  lines 
(1)  or  boundary  zones  (2) .  Boundary  lines  between  both  kinds  of 
areal  system  have  two  things  in  common:  Both  include  boundaries 
between  simple  areas,  and,  with  intrinsic  similarity  of  both  towns 
and  provinces,  both  separate  market  areas  for  the  same  marginal 
good.  The  same  Thunen  ring  lies  on  either  side  of  the  border, 
referring,  however,  to  different  towns;  and  with  economic  provinces 
we  find  on  either  side  of  the  boundary  market  areas  of  the  same 

13 


14 


Part  One.    Location 


good  that;  correspond  to  each  other  and  have  the  largest  necessary 
extension.  But  if  the  towns  or  provinces  are  of  different  size,  the 
goods  on  the  two  sides  of  the  boundary  are  also  different.  Any  kind 
of  Thiinen  rings  meet,  and  may  change  as  one  walks  along  the 
boundary.  Similarly,  when  the  economic  provinces  are  unequal, 
the  marginal  goods  are  different. 

The  distinction  between  boundary  lines  and  boundary  zones  is 
this:  The  former  constitute  a  sharp  boundary  between  two  towns  or 
major  cities  in  so  far  as  these  rival  each  other.  The  latter  exist 
only  between  major  cities,  and  indicate  the  boundary  area  in  which 
"  loophole  "  markets  are  found,  that  is,  markets  belonging  wholly 
to  neither  of  the  two  districts  even  though  both  are  by  nature  wholly 
similar.  They  arise  from  the  fact  that  where  markets  meet  district 
boundaries  empty  corners  appear  that  in  themselves  are  too  small 
to  afford  room  for  another  independent  enterprise,  and  that  can  be 
made  large  enough  only  by  combination  with  similar  corners  in 
the  adjoining  province.  We  shall  see  later  that  these  boundary 
zones  extend  from  the  edge  of  the  district  about  two  thirds  of  the 
way  toward  its  principal  city,  but  that  they  become  less  important 
as  they  approach  it.  Boundary  zones  are  not  distinguished  by  any 
particular  price  situation.  Boundary  lines  and  simple  boundaries 
introduced  under  (a) ,  on  the  contrary,  are  lines  of  equal  profit  to 
the  producer  or  of  equal  prices  to  the  consumer. 


B.  Selected  Problems  of  Location  ^ 

It  is  neither  possible  nor  really  necessary  to  answer  here  every 
problem  on  location  that  has  systematically  been  raised  in  the  pre- 
ceding section.  They  are  not  all  of  equal  importance,  and  the 
nature  of  the  solution  of  the  individual  cases  would  not  differ 
greatly.  It  will  suffice,  therefore,  to  demonstrate  a  few  typical 
methods  of  treating  the  problem.  Once  the  procedure  is  thoroughly 
grasped  there  will  be  no  difficulty  in  applying  it  to  other  and  more 
complex  situations. 

The  following  pages  will  discuss  two  groups  of  questions  con- 
cerning the  choice  of  location  seen  from  the  standpoint  of  the 
individual  economic  unit  (industrial  and  agricultural  location 
theory) ,  two  problems  on  the  agglomerations  of  locations  (forma- 
tion of  towns  and  belts) ,  and  two  divisions  of  the  general  theory  of 
location  (of  which  only  the  locational  equations  will  be  introduced 
in  this  part;  the  fundamental  discussion  on  economic  regions  will 
be  presented  separately) . 


1.  In  a  few  places  throughout  the  following  discussion  certain  findings  on  economic 
regions  have  been  anticipated,  whose  proof  cannot  be  given  until  Part  II. 

»5 


Chapter  4.     Industrial  Location  Theory 


a.     THE    GENERAL    PRINCIPLE 

The  location  of  an  industrial  enterprise  is  selected  by  the  entre- 
preneur. His  choice  rests  upon  subjective  considerations.  He  will, 
of  course,  bear  objective  facts  in  mind,  but  these  alone  cannot 
dictate  location.  Thus  it  is  conceivable  that  under  exactly  the  same 
external  conditions  two  entrepreneurs  may  choose  entirely  different 
locations.  The  available  range  ^  for  their  decision  depends  upon 
the  size  of  their  possible  entrepreneurial  profits.-  They  will  share 
only  the  formal  aim,  which  is  to  choose  their  location  so  that  the 
utility  shall  be  as  great  as  possible.  Whether  they  have  hit  upon 
the  right  one  can  be  determined  only  later,  of  course,  for  even  after 
mature  consideration  they  will  chose  "  with  their  fingers  crossed."  ^ 

L  Imitating  enterpreneurs  easily  forget  that  this  range  is  more  restricted  for  them 
than  for  the  abler  pioneers.  A  location  that  may  yield  the  latter  some  profit,  though 
not  the  greatest  possible,  may  result  in  losses  to  the  former.  Therefore  they  should  not 
simply  take  the  locations  of  leading  enterprises  as  a  guide,  or  without  further  thought 
attach  themselves  to  an  already  existent  agglomeration  of  their  industry. 

2.  Here  enter  all  those  eccentricities  that  skeptics  like  to  advance  as  examples  of 
the  irrationality  and  antitheoretical  nature  of  actual  events.  For  instance,  a  producer 
may  frequently  locate  his  plant  so  that  he  can  pursue  his  favorite  hobby  on  the  side. 
The  preference  of  English  businessmen  and  their  wives  for  life  in  the  south  of  England 
has  been  said  to  play  an  important  role  in  the  southward  migration  of  British 
industry.  (PEP,  Political  and  Economic  Planning:  Report  on  the  Location  of  Industry 
[London,  1939],  p.  46.)  But  as  long  as  such  a  capricious  choice  costs  no  more  than  the 
entrepreneurial  profit,  it  is  still  consistent  with  theory. 

3.  There  are  two  reasons  for  this:  the  practical  difficulty  of  determining  exactly 
under  given  conditions  how  good  a  site  really  is,  and  the  fundamental  impossibility  of 
foreseeing  how  these  conditions  will  change.  Dynamically  there  is  no  best  location, 
because  we  cannot  know  the  future.  What  follows  is  therefore  meant  to  apply  to  static 
conditions.  That  the  measurement  of  utility  itself  is  dubious  will  be  discussed  later. 

The  degree  of  uncertainty  connected  with  a  location  varies,  of  course.  The  scale 
runs  from  the  security  of  old  farms,  manorial  estates,  or  mercantile  establishments 
inherited  for  generations  that  have  seen  their  owners  through  all  vicissitudes;  through 
virtually  permanent  positions  that  their  occupants  hold  for  life  (rural  pastorates) ; 
through  the  multitude  of  industrial  enterprises  that  under  prudent  management  may 
last  for  a  few  generations,  or  may  move  away  or  collapse  at  any  moment;  down  to 
itinerant  folk  of  all  sorts— musicians  and  poets,  scientists  and  preachers,  inventors, 
mercenaries,  reformers  and  seekers  after  the  Holy  Grail,  for  all  of  whom  the  existing 
order  holds  no  place,  who  can  only  choose  between  being  ascetics  or  prostitutes  and 

i6 


Industrial  Location  Theory  17 

The  chosen  location  may  turn  out  to  be  only  subjectively  a  failure, 
or  even  objectively  so.  An  entrepreneur  fails  subjectively  when  the 
personal  success  expected  from  the  chosen  location  is  not  realized, 
objectively,  when  he  goes  into  bankruptcy  because  his  choice,  seen 
also  from  the  standpoint  of  the  economy  as  a  whole,  proved  to  be 
wrong.* 

b.     PRACTICAL    EXECUTION 

In  order  to  fix  exactly  the  point  of  greatest  utility  we  should 
have  to  bear  in  mind  more  considerations  than  would  be  scien- 
tifically possible,  let  alone  practically  convenient.  An  approximate 
formula  for  the  choice  of  a  location,  however,  depends  on  how 
many  of  the  factors  that  influence  a  careful  decision  are  eliminated. 
Obviously  all  irregular  influences  must  be  removed,  since  compre- 
hensible rules  can  be  established  only  for  the  effects  of  the  regular. 
If  we  disregard  all  locally  conditioned  priceless  utilities,  the  entre- 
preneur will  choose  the  location  of  greatest  real  profit.  If  we  discover 
no  spatial  regularity  in  the  price  level  of  the  things  he  consumes, 
which  will  certainly  be  true  for  corporations,  it  will  be  best  to 
eliminate  such  a  cost-of-living  pattern  also.  The  goal  will  then 
become  the  location  of  the  greatest  nominal  profit. 

§1.     One-Sided  Orientation 
a.    Cost  Orientation 

Nominal  profit  is  the  difference  between  money  cost  and  money 
receipts.  As  receipts  depend  on  many  irregular  factors,  industrial 
location  theory  has  generally  disregarded  them.  Thus  Weber  con- 
sidered demand  to  be  wholly  inelastic.  This  assumes  among  other 
things  that  an  areal  boundary  that  separates  neighboring  competitors 
is  fixed  once  and  for  all.  The  factory  would  then  be  situated  at  the 
point  of  lowest  c.  i.  f.  costs   (cost,  insurance,  freight) . 


whose  proper  location  is  the  highway,  where  they  are  torn  between  home  and  the 
world.  The  fate  of  List  is  repeated  every  day.  [Friedrich  List  (1789-1846) ,  a  German 
economist,  vigorously  championed  protective  tariffs  for  infant  industries,  customs 
unions,  and  government  development  of  railroads  and  merchant  marine.  Because  of 
his  views  he  was  forced  into  exile  for  several  years  and  upon  returning  to  Germany 
was  sentenced  to  imprisonment,  but  pardoned  when  he  promised  to  emigrate.  In  1825 
he  entered  the  United  States  and  later  became  a  citizen.  Because  of  illness  and  financial 
difiBculties  he  finally  took  his  own  life.— W.  H.  W.] 

4.  Bankruptcy  does  not  necessarily  mean  the  elimination  of  the  unfit,  but  mainly 
the  preservation  of  an  order  that  derives  its  dignity  through  its  distinction  from  chaos 
and  not  really  through  having  accomplished  something  just  or  meaningful  (except 
perhaps  the  maximum  of  free  will,  though  not,  as  was  formerly  believed,  the  maximum 
utility) .   See  below,  p.  92,  note  2. 


i8  Part  One.    Location 

1.      TRANSPORT    ORIENTATION 

The  cost  of  production  depends  upon  local  price  differences  and 
the  amounts  of  factors  of  production  and  other  things  required.  If 
these  inequalities  are  finally  abolished  by  the  ceteris  paribus  assump- 
tion, only  transport  costs  remain  to  be  minimized.  These  alone 
almost  always  show  spatial  regularity,  and  their  contribution  toward 
determining  location  has  therefore  become  the  principal  item  in 
the  ruling  theory. 

(aa)  The  Point  of  Minimum  Transport  Cost.  Location  theory 
up  to  now  recognizes  three  methods  for  determining  the  point  of 
minimum  transport  cost,  that  is,  the  place  where  total  freight  costs 
per  unit  are  lowest. 

1.  Construction  of  the  Point  of  Minimum  Transport  Cost  in 
the  Locational  Triangle  by  the  Proposition  of  Exterior  Angles.  This 
solution  was  first  discovered  by  W.  Launhardt,^  and  rediscovered  a 
generation  later  by  Alfred  Weber.°  In  recent  years  T.  Palander  ^  has 
contributed  an  extensive  discussion  of  this  solution.  The  method 
is  only  touched  upon  here,  because  it  is  of  neither  great  theoretical 
nor  great  practical  importance.  It  applies  only  when  the  number 
of  necessary  sources  of  materials  and  places  of  consumption  together 
amount  to  3,  and  freight  costs  are  proportional  to  weight  and 
distance. 

2.  The  Mechanical  Model.  Perforations  are  made  in  a  stiff  map 
at  the  sites  of  material  sources  and  markets.  Threads  bearing  deter- 
minate weights  are  passed  through  these  holes  and  tied  together  in 
one  knot.  The  position  of  rest  for  the  knot  is  the  desired  location 
of  production.  The  problem  of  finding  the  point  of  lowest  freight 
costs  is  identical  with  that  of  finding  the  position  of  equilibrium 
in  a  system  of  forces.  The  mathematical  proof  is  given  by  Palander.® 
The  weights  on  the  threads  are  proportional  to  the  quantities  to  be 
moved.  Let  A,  B,  and  C  be  raw  material  sites,  of  which  3,  2,  and 
0.5  tons  respectively  are  needed  to  produce  I  ton  of  finished  product; 
and  let  D,  E,  and  F  be  markets  consuming  80,  15,  and  5  per  cent  of 

5.  His  first  easily  accessible  paper  is  "  Die  Bestimmung  des  zweckmassigsten  Stand- 
orts  einer  gewerblichen  Anlage,"  Zeitschrift  des  Vereins  Deutscher  Ingenieure,  1882, 
pp.  106-115. 

6.  Alfred  Weber,  Ueber  den  Standort  der  Industrien,  Pt.  I  (Tubingen,  1909) . 
Translated  and  edited  by  C.  J.  Friedrich  as  Alfred  Weber's  Theory  of  the  Location 
of  Industries   (Chicago,  1928)  . 

7.  Tord  Palander,  Beitrdge  zur  Standortstheorie    (Uppsala,  1935)  ,  pp.  139-145. 

8.  Op.  cit.,  p.  141. 


Industrial  Location  Theory  19 

the  total  output  respectively.  Then  the  weights  for  the  points  A  to 
F  must  be  related  as  3  :  2  :  0.5  :  0.8  :  0.15  :  0.05.  (For  the  history 
and  bibliography  of  this  method  see  footnotes  5-7.)  The  field  of 
applicability  of  this  method  is  wider,  hov*^ever;  it  can  be  used  for 
any  desired  number  of  production  and  market  sites,  though  again 
only  when  freight  rates  are  proportional  to  distance. 

3.  Isodapanes.^  Alfred  Weber's  isodapanes  are  lines  of  equal 
total  freight  per  unit  of  product;  that  is,  lines  connecting  points  for 
which  a  definite  combination  of  hauls  is  equally  expensive.  The 
combination  consists  of  the  shipment  of  raw  materials  and  inter- 
mediate products  to,  and  shipments  of  the  finished  product  from. 


Fig.  2.    The  Construction  of  Isodapanes 

the  factory.  Isodapanes  must  be  distinguished  from  isovectures:  lines 
representing  equal  unit  freight  rates  for  simple  transport  to  and 
from  a  certain  place.  For  a  homogeneous  transport  surface,  isovec- 
tures are  concentric  circles  that  follow  one  another  at  equal  intervals 
for  similar  freight  differences.  They  are  proportional  to  distance  as 
one  proceeds  outward  from  the  center,  and  follow  one  another 
generally  at  increasing  intervals  for  a  graduated  tariff.  If  the  trans- 
port area  is  traversed  by  especially  cheap  lines  of  transportation 
(railroads,  canals) ,  combined  transports  result  (e.  g.,  by  rail  and 
truck)  ^°  and  the  isovectures  are  distorted,  Isovectures  serve  for  the 
construction  of  isodapanes.  They  are  drawn  for  the  transport  of  that 


9.  Palander   {op.  cit.,  p.  305)    has  reviewed  the  various  "  iso  "  lines. 

10.  Brilliantly  discussed  by  Palander,  op.  cit.,  pp.  337-360. 


20  Part  One.    Location 

quantity  of  goods  which  is  required  for  the  production  and  sale  of 
a  unit  of  finished  product.  Thus,  in  the  foregoing  example,  the 
isovecture  for  3  tons  is  drawn  around  A,  that  for  2  tons  around  B, 
and  so  on.  The  nearest  isovecture  around  A  is  the  line  up  to  which 
3  tons  of  the  particular  raw  material  can  be  shipped  for  the  total 
expenditure  of  1  monetary  unit  (isovecture  1) ;  the  next  line  con- 
nects the  places  to  which  the  shipment  of  3  tons  from  A  will  cost  2 
monetary  units  (isovecture  2) ,  and  so  on.  It  is  simplest  always  to 
derive  one  family  of  isodapanes  from  two  families  of  isovectures,  as 
shown  in  Figure  2.  On  the  assumption  of  a  freight  rate  proportional 
to  distance,  the  isovectures  1-12  are  drawn  around  A,  and  1-8 
around  B;  the  isodapanes  constructed  from  the  two  sets  of  isovec- 
tures are  drawn  in  as  the  broken  lines  9  and  10.  Isodapane  10,  for 
example,  connects  all  points  to  which  the  freight  of  3  tons  of  raw 
materials  from  A  and  of  2  tons  from  B  will  cost  together  10  mone- 
tary units.  On  it  there  lie,  for  instance,  the  points  of  intersection 
of  isovecture  4  around  A  and  of  isovecture  6  around  B,  and  also 
the  points  of  intersection  of  both  isovectures  5.  Next  a  group  of 
higher  order  isodapanes  is  constructed  in  exactly  the  same  way  until 
finally,  in  the  highest  group,  all  movements  of  goods  between  the 
production  site  looked  for  and  the  six  points  A  to  F  are  included. 
Of  these  highest  order  isodapanes  only  the  innermost  bearing  the 
lowest  cardinal  number  is  of  real  interest  in  the  present  context, 
because  it  surrounds  the  minimum  total  cost  of  transportation;  i.  e., 
the  most  advantageous  location  for  production.  Isodapanes  have  the 
advantage  over  the  mechanical  model  that,  like  it,  they  can  be  used 
for  any  desired  number  of  locations,  but,  in  addition,  they  can  be 
used  for  any  number  of  transportation  lines  and  transport  tariffs. 

4.  The  Principle  of  Substitution.  According  to  this  principle 
the  sum  of  freight  increases  equals  the  sum  of  freight  decreases  for 
infinitesimal  deviations  from  the  desired  location.^^  While  it  merely 
characterizes  the  minimum  point,  it  indicates  at  the  same  time  the 
possibility  of  calculating  it  from  the  equations  for  the  surface  repre- 
senting total  freight. 

(bb)  Limiting  Position  of  the  Point  of  Minimum  Transport 
Cost.  Ever  since  the  time  of  Weber,  special  interest  has  been  devoted 
to  those  special  situations  where  production  has  been  drawn  to  a 
favored  point.  In  addition  to  transshipment  points  and  nodal  points, 
we  also  designate  as  favored  points  the  sites  where  the  factors  of 

11.  A.  Predohl,  "Das  Standortproblem  in  der  Wirtschaftstheorie,"  Weltwirtschaft- 
liches  Archiv,  XXI    (1925)  ,  294-321.    The  principle  is  stated  on  p.  306. 


Industrial  Location  Theory  21 

production/-  consumers,  or  competitors  are  to  be  found. ^'  Under 
what  conditions  does  the  point  of  lowest  total  freight  costs  coincide 
with  one  of  these  favored  sites? 

Four  cases  may  be  imagined  with  a  tariff  proportional  to  distance. 
The  first  is  weight  ratios.  If  the  weight  on  one  of  the  threads  in  the 
mechanical  model  (p.  18)  is  greater  than  the  sum  of  the  remaining 
weights,  the  position  of  rest  for  the  system  of  forces  will  coincide 
with  the  point  of  insertion  for  the  large  weight.  In  the  Lorraine 
iron  industry,  for  example,  the  weight  ratios  before  World  War  I 
were:  3  tons  of  ore  +  1  ton  of  coke  =  1  ton  of  pig  iron.  Thus  the 
weight  of  the  ore  was  greater  than  the  sum  of  the  two  other  weights. 
The  attraction  of  the  Lorraine  minette  basin  would  have  been  even 
greater  had  not  the  freight  rate  for  coke  from  the  Ruhr  to  Lorraine 
exceeded  that  for  the  shipment  of  ore  from  Lorraine  to  the  Ruhr." 
The  poorer  the  ores  that  have  to  be  smelted,  the  greater  the  attrac- 
tion of  their  deposits.  Hence  the  iron  industry  moves  today  more 
and  more  toward  the  ore.  A  typical  example  of  weight-conditioned 
attraction  toward  the  consumer  is  offered  by  the  brewing  industry. 
The  weight  of  the  water  added  is  greater  than  the  weight  lost  by 
hops,  malt,  and  fuel. 

The  relative  positions  of  the  various  locations  are  the  second 
reason  for  the  coincidence  of  the  point  of  minimum  transport  cost 
with  one  of  the  favored  points.  What  has  just  been  described  occurs 

12.  If  these  are  present  but  only  in  insufficient  number  one  can  speak  of  a  favored 
point  or  site  only  with  reservations. 

13.  There  may  be  some  doubt  whether  a  central  location  between  neighboring 
competitors  belongs  here.  Such  a  location  may  be  highly  important  as  a  guess  in 
respect  to  a  possible  general  neighborhood  but  it  is  difficult  to  define  in  theory,  since 
it  is  not  a  stable  point;  indeed,  under  realistic  assumptions  such  a  point  can  be  defined 
only  through  maximization  of  profits.  Such  an  intermediate  location  is  probable  if, 
first,  in  transport  orientation  the  freight  rate  on  raw  material  is  low  compared  with 
that  on  the  finished  product  (in  the  German  railway  tariff  the  highest  rate  for  manu- 
factured goods  by  the  carload  is  almost  five  times,  the  less-than-carload  rate  almost 
thirty  times,  as  high  as  for  coal!) ,  so  that  production  would  be  carried  out  exactly 
at  the  center  of  consumption;  if,  second,  in  orientation  by  total  costs  instead  or  besides, 
location  of  raw  material  and  labor  are  about  evenly  distributed;  if,  third,  in  orien- 
tation by  return  the  buyers  are  scattered  (at  the  desired  point  the  sales  cone  would 
have  to  be  intersected  least  by  the  neighboring  ones)  ;  or  if,  fourth,  in  orientation  by 
profits  everything  coincides:  high  freight  on  manufactured  goods,  and  wide  dispersion 
of  raw  material  sites,  labor,  and  the  markets.  This  case  leads  to  production  for  a  well- 
rounded  exclusive  territory.  Eggers  and  Umlauf  have  called  this  "  area-bound  "  pro- 
duction.  Part  II  will  be  devoted  to  this  topic. 

14.  H.  Schumacher,  "  Die  Wanderung  der  Grossindustrie  in  Deutschland  und  in 
den  Vereinigten  Staaten,"  Schmollers  Jahrbuch,  1910,  pp.  451-482.  Buchman  et  al.. 
Die  Standorte  der  Eisen-  und  Stahlindustrien  der  Welt   (Berlin,  1927)  . 


22  Part  One.     Location 

not  only  when  one  of  the  weights  exceeds  the  sum  of  the  others, 
but  also  when  it  exceeds  their  resultants.  The  resultant  for  any 
given  weight  depends  on  the  relative  positions  of  the  points  of 
insertion  of  the  weights." 

Third,  established  lines  of  communication  have  the  result  that 
the  costs  of  transportation  are  always  smallest  at  one  of  the  perfora- 
tions (location  of  raw  material  or  of  consumption)  or  nodes,  as  can 
be  readily  seen  on  the  mechanical  model.  Only  at  such  favored 
places  can  the  opposing  forces  affect  each  other  by  altering  the  angle 
of  attack,  whereas  between  these  points  they  remain  constant.  Hence 
the  nodes  have  the  advantage  that  from  them  a  larger  number  of 
places  can  be  directly  reached  than  from  other  points,  which  might 
perhaps  be  preferred  if  a  transport  area  existed. 

The  first  three  causes  for  the  limiting  special  locations  consisted 
in  a  reduction  of  transport  cost.  The  fourth  cause  lies  in  a  saving 
of  transshipment  cost.  This  factor,  among  others,  accounts  for  the 
location  of  industries  at  transport  junctions,  including  seaports. 
Even  where  transports  do  not  pass  a  transshipment  point,  the  cost 
of  reloading  would  nevertheless  be  saved  if  the  production  site  were 
moved  directly  to  the  source  of  a  factor  of  production  instead  of 
simply  near  it.  This  shift  will  occur  as  long  as  the  increase  in  line- 
haul  costs  is  less  than  the  saving  in  terminal  costs. 

We  now  replace  the  simple  tariff  proportional  to  distance  by 
differential  tariffs.  First,  according  to  the  type  of  goods:  The  freight 
rate  for  the  finished  good  is  often  higher.  This  works  out  exactly  as 
though  the  ordinary  rate  prevailed  but  the  finished  product  were 
heavier  than  it  actually  is  (Weber's  "  ideal  "  weight) .  It  alters 
nothing  in  our  analysis  except  that  location  at  the  site  of  consump- 
tion becomes  more  probable.  Not  so,  secondly,  when  rates  are 
graduated  according  to  length  of  haul.  Graduated  tariffs  favor  ship- 
ment over  long  distances  and  hence  favor  as  locations  the  starting 
points  and  terminals  of  transportation  systems  (location  of  raw 
materials  or  of  consumption)  rather  than  intermediate  or  transship- 
ment points.^" 

15.  For  the  simple  case  of  the  location  triangle  I  refer  as  an  example  to  Palander's 
figure  8  (op.  cit.,  p.  144) .  If  a  consumption  site  K  lies  in  one  of  the  cross-hatched 
areas,  we  have  a  normal  case:  the  site  of  production  lies  within  the  location  figure. 
If  K  lies  in  the  dotted  area,  goods  are  produced  at  the  point  of  consumption.  If  it 
lies  in  the  area  of  broken  lines,  goods  are  produced  at  the  source  of  raw  material. 
Many  scattered  areas  of  consumption  easily  give  the  raw  material  site  the  prepon- 
derance of  influence  in  the  location  of  production. 

16.  The  contrast  with  a  straight  mileage  tariff  is  well  brought  out  by  Palander's 
figures    {op.  cit.,  p.  318)  .    The  legends  must,  however,  be  transposed. 


Industrial  Location  Theory  23 

The  recent  development  of  automobile  transportation  counter- 
acts some  of  the  factors  discussed  that  influence  the  limiting  special 
location.  It  undermines  the  preferred  position  of  railway  stations 
in  general  and  that  of  favored  special  points  in  particular.  The 
advantages  of  transshipment  points  are  less  frequently  felt  because 
transshipment  is  less  frequent  when  motor  trucks  are  employed. 
Location  near  consumption— whether  it  is  concentrated  in  large  cities 
or  distributed  over  open  country— becomes  less  advantageous  because 
with  competition  truck  rates  are  regulated  more  by  immediate  cost 
than  by  "  what  the  traffic  will  bear."  Thus  it  is  hardly  possible  to 
burden  finished  goods  with  higher  rates.  Markets  and  locations  of 
raw  materials,  finally  lose  their  power  to  attract  when,  as  in  the  case 
of  the  motor  truck,  mileage  tariffs  supplant  graduated  freight  rates. ^' 

To  this  extent  the  truck  has  a  decentralizing  effect  on  the  location 
of  industry.  It  breaks  up  agglomerations  that  depend  only  on  differ- 
entiated freight  tariffs  but,  under  conditions  still  to  be  discussed, 
it  encourages  agglomerations  that  depend  upon  lower  production 
costs  by  eliminating  scattered  rural  locations. 

2.       ORIENTATION     ACCORDING    TO     PRODUCTION     COSTS 

Production  costs  by  themselves  may  sometimes  determine  loca- 
tion exclusively,  but  if  so,  always  in  marginal  situations.  The 
generally  indefinite  technical  orientation  by  production  must  be 
separated  from  this  case.  Only  where  one  or  a  combination  of 
several  factors  of  production  are  exhaustible,  immobile,  and  unique, 
does  production  necessarily  occur  at  this  location  if  at  all.  In  the 
main,  these  will  be  instances  of  resources  whose  occurrence  in  the 
necessary  minimum  quantities  is  especially  rare,  of  some  special 
climate,  or  of  gifted  men  who  refuse  to  migrate. 

3.   ORIENTATION  ACCORDING  TO  TOTAL  COSTS 

(aa)  Location  of  Lowest  C.LF.  Costs.  As  a  rule  the  costs  of 
production  cannot  be  separated  from  the  freight  cost  on  raw  material, 
and  often  it  is  not  desired  to  separate  them  from  the  freight  cost  on 
the  finished  product.  In  such  cases  they  affect  location  only  in  com- 
bination with  the  latter,  e.  g.,  when  several  scattered  raw  materials 
have  to  be  combined,  or  when  several  sources  of  supply  are  available. 
In  our  examples  on  page  18  let  there  be  two  sources  for  the  first, 
mobile  raw  material,  for  which  the  cost  at  /ij  is  10  marks  per  ton 

17.  Thus  the  automobile  is  superior  to  the  railroad  for  short  hauls,  for  express 
freights,  and  for  goods  on  which  freight  rates  are  high. 


OA  Part  One.     Location 

whereas  in  remote  A  2  it  is  only  5  marks.  By  ordering  from  A  2, 
15  marks  on  every  ton  of  finished  product  can  be  saved.  But  let 
the  total  freight  per  ton  of  finished  product  for  the  combination 
Ai,B-  ■  F  at  the  point  of  minimum  transport  cost  be  20  marks 
less  than  at  the  minimum  point  for  the  combination  A2,B  ■  ■  F. 
The  more  expensive  but  nearer  source,  A^,  would  therefore  be  pre- 
ferred. Hence  freight  costs  decide  the  choice  among  sources,  and 
production  costs  ^^  the  choice  among  points  of  lowest  freight  rates. 
In  short,  the  most  favorable  location  depends  upon  both,  and 
therefore  upon  total  costs.^^ 

(bb)  Special  Location  of  the  Point  of  Lowest  Total  Cost.  Here 
many  things  must  be  distinguished.  First,  total  costs  may  attract  an 
enterprise  to  a  favored  point  even  though  neither  production  costs 
nor  cost  of  distance  is  a  minimum  there,  provided  that  the  sum  of 

18.  Spatial  differences  in  production  costs  rest  upon  the  fact,  as  Ohlin  has  fre- 
quently emphasized,  that  the  factor  endowment  of  different  regions  varies,  and  that 
these  factors  are  combined  in  varying  proportions  and  thus  affect  production  in 
different  degrees.  However,  spatial  price  differences  are  not  simply  the  result  of  local 
differences  in  scarcity.  Because  of  the  mobility  of  the  factors  of  production  and  of 
their  products,  the  relative  scarcities  themselves  are  a  result  of  the  particular  spatial 
price  system.  It  is  necessary  to  emphasize  interdependence  at  this  point,  instead  of 
merely  citing  physical  factors  (climate,  natural  resources,  human  characteristics)  as  causes 
of  local  differences  in  production  costs.  But  it  will  not  do  to  reduce  spatial  price 
differences  entirely  to  variations  in  freight  cost,  and  thus  orientation  according  to  total 
costs  to  transport  orientation,  since  the  price  differences  may  be  smaller  than  the 
freight  costs.  The  difficulty  could  be  surmounted,  to  be  sure,  by  pushing  the  signifi- 
cance of  space  too  far,  and  developing  the  whole  theory  of  production  as  a  theory  of 
transportation.  Obviously  every  step  in  production  could  always  be  reduced  in  the 
last  analysis  to  spatial  movement. 

19.  Again  the  substitution  principle  characterizes  the  minimum  point:  For  small 
changes  in  location,  the  sum  of  cost  increases  must  equal  the  sum  of  cost  decreases.  If 
costs  were  known  as  a  function  of  latitude  and  longitude,  their  minimum  point  could 
be  determined  on  principle  algebraically  instead  of  by  Weber's  geometrical  solution. 
Predohl  (loc.  cit.)  introduced  the  marginal  principle  into  the  theory  of  industrial 
location.  The  substitution  equilibrium  is  harder  to  define  here,  however,  than  in  price 
theory.  Predohl  to  the  contrary  (op.  cit.,  p.  314,  but  in  agreement  with  other  passages), 
it  does  not  matter  that  equally  priced  amounts  of  means  of  production,  whose  price 
varies  locally,  may  be  substituted  for  one  another  without  change  in  physical  return 

(which  here  includes  transportation  to  the  buyer) .  It  is  not  the  change  in  physical 
cost  (which  may  be  restricted  to  transportation  or  be  wholly  absent)  that  is  relevant, 
but  in  money  cost;  and  not  in  two  factors,  but  in  two  combinations  of  all  factors 
(which  may  differ  in  amount  and/or  value) .  The  entire  combination  varies  even  with 
small  changes  in  location  (in  contradistinction  to  substitution  at  the  same  place)  and 
its  total  costs  must  remain  constant.  With  larger  displacements,  say  to  a  place  of 
cheap  labor,  total  costs  may  nevertheless  decrease.  As  soon  as  there  are  several  points 
of  minimum  cost  the  marginal  principle  fails  to  indicate  the  best  (discontinuous 
substitution) . 


Industrial  Location  Theory  ^5 

the  two  costs  is  a  minimum.  Second,  in  cases  that  remain  indeter- 
minate in  respect  to  production  orientation,  total  costs  permit  a  deci- 
sion as  to  where,  if  anywhere,  the  special  location  is  reached.  It  may, 
for  example,  happen  that  a  factor  of  production  is  immobile  but 
not  irreplaceable,  or  that  it  is  found  in  several  places.  The  condi- 
tions of  production  decide  only  that  in  the  case  of  replaceable  factors 
some  special  location  may  be,  and  in  the  case  of  more  frequently 
found  factors  certainly  will  be,  chosen.  Only  total  cost  can  decide 
among  the  various  possibilities.  Again  Weber's  isodapanes  are 
employed.^"  But  instead  of  giving  each  of  the  highest  isodapanes 
the  cardinal  number  that  corresponds  to  the  total  freight  for  each 
unit  of  product  when  it  is  produced  on  a  particular  isodapane,  we 
may  set  down  the  difference  between  this  figure  and  the  freight 
costs  at  the  minimum  point.  This  new  number  indicates  by  how 
many  monetary  units  the  total  freight  costs  per  unit  of  product 
increase,  when  production  is  moved  away  from  the  optimum  trans- 
port point  onto  the  corresponding  isodapane. 

If,  for  example,  local  wage  differences  are  to  be  considered,  we 
can  indicate  in  the  same  way  by  how  much  the  labor  cost  per  unit 
is  greater  or  less  than  at  the  point  of  lowest  freight  costs.-^  Instead 
of  at  the  place  of  lowest  freight  cost,  the  plant  will  then  be  set  up 
where  the  saving  in  wages  less  the  additional  freight  costs  is  greatest. 

Third,  where  production  is  technically  restricted  to  a  unique 
location,  and  where  location  by  partial  cost  leads  to  a  special  location, 
this  special  location  will  be  necessarily  confirmed  by  the  effect  of 
total  cost.  The  special  location  may  perhaps  be  confirmed  by  the 
effect  of  total  cost  when  the  plant  has  been  transport  oriented. 

Fourth,  if  costs  of  transport  alone  lead  to  an  unequivocal  ^^  special 
location,  this  location  can  be  shifted  to  another  favored  point  as 

20.  A.  Weber,  op.  cit.,  pp.  100-103;  English  ed.,  pp.  102-104. 

21.  Occasionally  the  spatial  picture  of  wages  will  be  so  regular  that  isotims  of 
labor  can  also  be  drawn;  that  is,  lines  connecting  points  of  equal  wages.  Moreover, 
as  "  iso-lines  "  or  "  contour  lines  "  can  be  interpolated  within  certain  limits,  L.  von 
Bortkiewicz  was  probably  not  correct  on  this  point  in  his  otherwise  wholly  pertinent 
criticism  of  Weber.  Bortkiewicz  prefers  empirical  calculation  even  when  nothing  but 
freight  and  labor  costs  are  taken  into  account,  because  isodapanes  themselves  are  simply 
made  up  of  similar  individual  empirical  calculation  and  only  afterwards  compared  with 
individual  labor  markets,  which  is  a  more  complex  procedure  than  the  finding  of 
freight  cost  in  general  for  these  sites  alone.  ("  Eine  geometrische  Fundierung  der  Lehre 
vom  Standort  der  Industrien,"  Archiv  filr  Soziahvisseuschaft,  XXX  [1910],  759  ff.  The 
criticism  is  found  on  page  770.) 

22.  A  special  location  according  to  transport  orientation  is  almost  always  unequi- 
vocal. Even  with  several  minimum  points,  one  will  generally  be  the  cheapest  because 
there  are  several  sources  of  supply  to  choose  from. 


26 


Part  One.    Location 


soon  as  the  prices  of  factors  are  taken  into  consideration  that  either 
are  found  in  different  places  or,  though  mobile,  do  not  give  rise  to 
freight  cost.^^  Whenever  production  costs  by  themselves  lead  to  an 
unequivocal  special  location  that  is  determined  not  exclusively  on 
technical  but  perhaps  only  on  economic  grounds,^*  the  simultaneous 
consideration  of  transportation  costs  may  likewise  lead  to  removal 
to  another  favored  point. 

Finally,  orientation  by  total  costs  may  even  eliminate  the  special 
location  in  such  cases  instead  of  merely  changing  it. 

j3.    Orientation  by  Gross  Receipts 

1.     LOCATION    OF   THE    MOST    FAVORABLE    MARKET 

A  plant  can  be  established  at  a  place  where  revenue  is  greatest 
rather  than  where  outgo  is  smallest.^^  Still  more  one-sided  than  the 
choice  of  the  place  of  largest  sales  would  be  establishment  according 
to  one  of  their  components,  quantity  and  price.  Orientation  by 
quantity  would  look  more  toward  the  number  of  buyers,  orientation 
by  price  toward  their  purchasing  power.  The  former,  therefore, 
would  favor  populous  districts;  the  latter,  prosperous  ones;  both 
prefer  a  location  away  from  competition. 

2.     SPECIAL    LOCATION    OF    THE    POINT    OF    GREATEST 
GROSS    RECEIPTS 

Regard  for  gross  receipts  alone  forces  production  to  the  location 
of  the  consumer,  if  the  market  is  technically  tied  to  the  buyer  (the 
corresponding  phenomenon  on  the  expenditure  side  is  production 
tied  to  an  immobile  factor  of  production) ,  and  if  purchasers  cannot 
or  will  not  change  their  location  (the  corresponding  phenomenon  is 
irreplaceable  production  factors.^'') .    If  such  areas  of  consumption 

23.  Local  taxes,  capital,  and  labor,  for  example.  Capital  is  almost  never  immobile, 
and  labor  at  most  in  respect  to  definite  kinds  and  definite  amounts.  But  the  cost  of 
changing  their  locations  cannot,  except  for  commuters,  be  treated  as  are  other  trans- 
portation costs.    It  is  incurred  only  once  and  connected  with  the  locality  in  question. 

24.  When  all  production  elements  are  present  in  one  or  several  places  and  thus  no 
transportation  is  technically  necessary  for  purposes  of  production,  the  only  or  cheapest 
source  will  be  chosen  in  orientation  by  production,  whereas  in  orientation  by  total  costs 
the  combination  of  factors  from  different  places,  or  a  location  nearer  the  market,  may 
be  still  more  advantageous. 

25.  ".  .  .  in  the  absence  of  decisive  natural  factors  .  .  .  industries  tend  to  be  located 
within  easy  reach  of  the  market."  Royal  Commission  on  the  Distribution  of  the  Indus- 
trial Population   (Barlow  Commission)   Report   (London,  1940)     (Cmd.  6153)  ,  p.  48. 

26.  As  a  rule  the  location  of  consumers  depends  in  turn,  at  least  in  principle,  on 
the  local  prices  of  the  production  technically  tied  to  them. 


Industrial  Location    Tlit^ory  27 

exist  everywhere  (the  corresponding  phenomenon  with  natural  fac- 
tors is  ubiquitous  occurrence) ,  the  fact  of  a  special  location  means 
nothing;  if  several  possible  locations  exist,  the  special  location  is 
technically  indeterminate;  that  is,  it  is  a  necessary  but  not  sufficient 
condition  for  the  choice  of  a  location.  Then  receipts  are  the  gov- 
erning factor.  The  special  location  is  technically  unequivocal  only 
when  all  buyers,  or  at  least  a  sufficient  number,  live  in  one  place. 

§2.    The  Correct  Procedure 
a.    Orientation  by  Profit 

In  so  far  as  they  dominate  in  practice,  all  the  points  of  view  so 
far  discussed  may  perhaps  explain  an  actual  location,  but  except  in 
special  cases  no  single  one  shows  the  right  location.  This  depends 
neither  upon  expenses  nor  upon  gross  receipts  alone,  to  say  nothing 
of  any  individual  cost  or  receipt  component.  Their  significance 
may  well  be  considered  singly  at  the  beginning  of  the  analysis,  but 
the  final  and  sole  determining  factor  is  their  balance:  the  net  profit. 
In  a  free  economy,  the  correct  location  of  the  individual  enterprise 
lies  where  the  net  profit  is  greatest.^^ 

Of  course,  even  the  procedures  discussed  above  represented 
attempts  to  find  this  optimum  point.  For  when  receipts,  say,  are 
given,  the  location  of  the  greatest  profit  coincides  with  that  for  the 
lowest  c.  i.  f.  costs.  But  a  consideration  of  the  variability  of  gross 
revenue  should  make  use  beyond  a  one-sided  orientation  by  costs;  we 
should  not,  with  Weber,  regard  gross  revenue  as  constant  by  assuming 
a  given  demand  and  price.  Actually,  demand  varies  with  price  ^^  in 
part  directly,  in  part  via  the  size  of  the  market  area;  and  it  varies 
also  with  the  site  of  production  chosen.  The  connection  between 
price,  demand,  and  location  is  such  that  for  each  possible  factory 
price,  for  example,  the  greatest  total  demand  will  be  realized  with 
a  different  location  of  the  plant,  because  with  every  change  in  price 
the  market  area  assumes  another  form  (even  if,  as  will  usually 
happen,  neighboring  competitors  do  not  change  their  locations  too) , 
and  because  the  demand  of  individual  markets  changes  in  different 
proportions.  Even  in  the  simple  case  of  a  linear  demand  curve,  an 
increase  in  price  would  restrict  the  demand  from  distant  points  by  a 

27.  This  does  not  exclude  deviations  for  extra-economic  reasons,  in  so  far  as  profits 
permit. 

28.  In  other  words,  sales  rise  as  prices  fall:  (1)  at  the  expense  of  competitors  and 
(2)  at  the  expense  of  other  products.  Not  only  does  the  demand  curve  shift  to  the 
right,  but  actual  demand  moves  downward  on  the  new  curve  as  well. 


28  Part  One.    Location 

larger  percentage  than  that  from  nearer  ones.  The  factory  location 
that  would  result  in  the  greatest  total  demand  would  thus  be  more 
strongly  affected  by  the  location  of  neighboring  markets  when 
prices  are  high  than  when  they  are  low.  That  is,  the  optimum 
location  would  shift  with  each  change  in  price.  As  soon  as  this 
variability  in  demand  is  taken  into  account  ^^  all  of  Weber's  con- 
structions on  the  supply  side  collapse  again.^"  For  it  becomes 
meaningless  to  wish  to  find  the  point  of  lowest  cost.  The  minimum 
transport  point  and  isodapanes  cease  to  exist.  The  minimum  point 
vanishes  because,  as  soon  as  the  boundaries  of  the  market  area  are 
changeable,  the  average  freight  costs  would  be  smallest  if  nothing 
were  sold  beyond  the  location  of  the  factory— indeed,  if  the  factory 
itself  were  finally  to  disappear!  Isodapanes,  on  the  other  hand,  can 
be  constructed  only  when  a  shift  in  location  does  not  itself  bring 
about  a  shift  in  demand. 

It  is  hardly  necessary  to  go  further  into  this  matter.  Weber's 
solution  for  the  problem  of  location  proves  to  be  incorrect  as  soon 
as  not  only  cost  but  also  sales  possibilities  are  considered.  His 
fundamental  error  consists  in  seeking  the  place  of  lowest  cost.^^ 

29.  A.  Robinson  has  recently  criticized  this  omission  by  Weber.  Review  of  S.  R. 
Dennison,  The  Location  of  Industry  and  the  Depressed  Areas  (Oxford,  1939) ,  in 
Economic  Journal,  L   (1940) ,  267. 

30.  This  does  not  exclude  the  possibility  that  isodapanes  may  aid  in  the  deter- 
mination of  locations  not  only  of  production,  but  also  of  consumption,  and  of  raw 
materials,  whenever  two  of  the  three  categories  of  location  are  given.  (See  Palander, 
op.  cit.,  pp.  159  ff.)  In  the  first  case,  local  wage  differences  may  be  taken  into  account, 
as  described  above;  in  the  other  two  cases,  differences  in  f .  o.  b.  cost  of  materials. 
(Ibid.,  pp.  162-165.) 

In  the  intermediate  case,  the  problem  may  be  to  include  simultaneously  both  kinds 
of  local  differences  in  manufacturing  costs  in  the  calculations.  This,  too,  can  be  done 
in  principle.  All  isodapanes  (i.  e.,  lines  of  equal  freight  cost)  merely  become  isotims 
(i.  e.,  lines  of  equal  price,  or,  in  this  case,  of  equal  total  unit  cost) .  With  their  help 
we  can  determine  the  area  for  which  any  particular  combination  of  production  sites 
and  raw  material  sources  (at  least  with  constant  cost)  will  be  superior  to  every  other 
combination.  The  lines  separating  such  areas  are  indifference  lines,  or  "isostants," 
i.  e.,  lines  of  minimum  cost  points.  However,  one  must  not  overlook  the  fact  that  such 
a  construction  presupposes  a  knowledge  of  production  locations,  and  is  therefore  not 
suited  to  their  discovery.  Nor  does  it  permit  consideration  of  the  influence  of  changing 
demand  upon  costs  any  more  than  does  the  construction  of  isodapanes. 

31.  This  applies  also  to  all  modern  location  theories  (those  of  Predohl,  Palander, 
and  Ritschl  among  others)  in  so  far  as  they  are  based  on  Weber.  See  my  review  of 
Palander's  Beitrdge  zur  Standorttheorie  in  Schmollers  Jahrbuch,  1938,  and  my  reply  to 
Ritschl,  "  Um  eine  neue  Standorttheorie:  Eine  Auseinandersetzung  mit  Ritschl,"  Welt- 
wirtschaftliches  Archiv,  LIV   (1941),  I»-ll*. 

This  by  no  means  excludes  the  incorporation  into  a  new  location  theory  o*f  parts 
of  his  theory  which,  though  destroyed  as  a  whole,  nevertheless  is  a  great  achievement. 


Industrial  Location  Theory  29 

This  is  as  absurd  as  to  consider  the  point  of  largest  sales  as  the 
proper  location.  Every  such  one-sided  orientation  is  wrong.  Only 
search  for  the  place  of  greatest  profit  is  right, 

But  where  is  this  to  be  found?  A  geometrical  solution  becomes 
impossible  as  soon  as  price  and  quantity  are  added  to  the  two 
spatial  variables,  for  it  can  be  applied  to  three  variables  at  most. 
Yet  algebraic  treatment  leads  to  equations  of  an  insoluble  degree. 
This  complexity  stems  from  the  facts  that,  as  already  explained, 
there  is  more  than  one  geographical  point  where  the  total  demand 
of  a  surrounding  district  is  at  a  maximum,  and  that  from  these 
points  outward  total  demand  does  not  decrease  according  to  a 
simple  function.32  \Ye  are  thus  reduced  to  determine  separately 
for  every  one  of  a  number  of  virtual  factory  locations  the  total 
attainable  demand,  and  for  similar  reasons  the  best  volume  of  pro- 
duction as  a  function  of  factory  price  (market  and  cost  analysis) . 
The  greatest  profit  attainable  at  each  of  these  points  can  be  deter- 
mined from  the  cost  and  demand  curves,  and  from  this  the  place 
of  greatest  money  profit,  the  optimum  location,  can  be  found. 
Now  the  procedure  is  no  longer  theoretical,  however,  but  simply 
empirical  testing,  since  the  result  holds  only  for  the  locations  actually 
examined  and  cannot  be  interpolated.  As  all  points  in  an  area  can 
never  be  analyzed  in  this  manner,  we  cannot  exclude  the  possibility 
that  among  the  locations  not  examined  there  may  be  one  that  would 
yield  a  higher  return  than  the  most  advantageous  of  those  inves- 
tigated. There  is  no  scientific  and  unequivocal  solution  for  the 
location  of  the  individual  firm,  but  only  a  practical  one:  the  test 
of  trial  and  error.  Hence  Weber's  and  all  the  other  attempts  at  a 
systematic  and  valid  location  theory  for  the  individual  firm  were 
doomed  to  failure. 

For  example,  Weber's  method  could  be  employed  in  deciding  between  dispersed  settle- 
ment of  farmers  and  village  settlement.  For  in  this  case  demand  is  actually  given  as  a 
first  approximation  as  far  as  the  location,  amount,  and  market  price  and  the  number 
of  products  are  concerned  (but  see  p.  60,  note  41) .  Thus  economically  it  remains  only 
to  locate  the  farms  in  such  a  way  that  the  total  costs  of  transportation  to  the  farmer 
as  producer,  vendor,  and  consumer  are  minimized. 

Advocates  of  the  classical  theory  of  international  trade  which  regards  countries  as 
points  and  the  market  area  as  given  can  explain  the  international  division  of  labor 
also  by  means  of  the  minimum  transport  point  (see  W.  H.  Dean,  The  Theory  of  the 
Geographic  Location  of  Economic  Activities  [Ann  Arbor,  1938],  pp.  24  ff.,  from  the 
dissertation) ,  or  at  least  introduce  the  conditions  of  transportation  into  the  theory  of 
comparative  cost. 

32.  Nor  does  a  substitution  equilibrium  prevail  here  any  longer.  Even  with  small 
departures  from  the  best  location  the  cost  may  change,  if  their  change  is  as  great  as 
that  of  the  proceeds. 


^o  Part  One.     Location 

Yet  science  does  offer  something  to  the  practical  investigator  of 
locations.  First,  it  teaches  him  to  avoid  the  errors  of  one-sided 
orientation,  wherein  generally  an  investigator  may  arrive  at  wrong 
conclusions  more  often  than  right  ones.  Second— and  this  is  really 
the  most  important— the  theory  and  statistics  of  areas  with  or  without 
insufficient  locations  (that  is,  our  theory  seen  from  the  practical 
side  of  the  individual  firm)  indicates  not  at  what  spot,  but  in  what 
neighborhood,  a  new  location  must  be  sought.  For  the  actual  choice 
we  can  at  least  provide  a  list  of  favored  points  that  should  by  all 
means  be  appraised  in  addition  to  the  approximate  center  of  gravity 
of  the  market  area,  even  though  it  might  be  advisable  to  avoid  them 
since  their  market  areas  are  often  more  than  saturated.  But  there 
might  be  so  many  of  these  points  that  it  would  be  worth  while  to 
know  which  ones  deserved  further  examination.  Here,  too,  theo- 
retical considerations  help,  together  with  the  findings  of  statistics 
and  the  results  of  practical  experienced^ 

33.  To  that  end  it  is  necessary  to  determine  on  the  cost  side  which  point  of  supply 
of  production  factors  offers  the  greatest  saving  as  a  location.  Thus  for  each  individual 
cost  items  we  must  know:  (a)  their  shares  in  the  total  costs  (chief  cost  factors  of  an 
industry) ;  (b)  the  extent  of  their  geographical  differences  (cheapest  sources  for  the 
main  cost  factors  as  compared  with  the  most  expensive) .  The  former  can  be  only 
approximately  calculated  since  the  share  itself  varies  from  place  to  place.  In  the 
latter,  geographical  price  differences  include  the  costs  of  transportation.  For  most  cost 
factors  the  price  will  be  lowest  at  one  of  their  points  of  supply.  Local  taxes,  of  course, 
have  no  point  of  supply;  workers  may  be  willing  to  accept  lower  wages  in  an  attractive 
place  to  which  they  must  first  migrate.  Goods  may  be  cheaper  away  from  the  place 
where  they  are  produced  because  of  dumping  or  of  smaller  trade  margins.  The  saving 
in  costs  is  presumably  greatest  where  those  factors  are  cheapest  (a)  whose  share  in 
total  costs  and  (b)  whose  geographical  price  differences  are  especially  large;  with 
factors  where  only  (a)  or  (b) ,  or  neither,  has  a  high  value  considerable  savings  are 
less  probable.  Whether  this  first  presumption  was  justified  can  be  determined  for  any 
given  place  only  after  the  cost  of  factors  that  are  not  particularly  cheap  is  taken  into 
account.  However,  to  calculate  total  production  costs  one  must  include  demand,  whose 
extent  often  determines  the  height  of  the  costs  and  always  decides  whether  they  can  be 
borne.  Thus  one  ends  up  with  an  unavoidable  calculation  of  the  chances  of  profit  in  a 
particular  locality.  As  a  location  where  the  most  important  cost  factor  was  especially 
cheap  may  nevertheless  prove  a  failure  in  the  end  the  suggestion  of  such  a  location 
can  be  only  a  hint,  worth  following  up,  but  nothing  more.  Similarly,  and  with  results 
of  equal  value,  places  may  be  selected  from  the  standpoint  of  demand  and  appraised 
where  the  product  presumably  might  bring  a  particularly  high  price  or  command  a 
particularly  large  market.  But,  above  all,  points  more  or  less  in  the  center  of  their 
expected  sales  areas  should  be  considered,  and  even  before  that  the  favored  points  in 
their  vicinity. 

These  reflections  are  applicable  to  entire  industries.  If  systematic  lists  are  prepared 
of  the  characteristics  of  various  industries  (technical  restrictions,  cost  structure,  market 
conditions) ;  of  various  sites  (supplies,  prices,  location) ;  and  of  locations  already 
appraised,  the  locations  and  possibilities  of  dislocation  that  are  especially  probable  or 


Industrial  Location  Theory  3* 

Finally,  the  effect  of  single  location  factors,  and  the  co-operation 
of  at  least  the  most  important  ones,  can  be  shown  in  a  series  of 
typical  though  greatly  simplified  cases.  This  would  aid  directly  in 
the  discussion  of  practical  location  questions,  or  at  least  provide  a 
model.^*  The  irregularity  of  even  such  standardized  situations  makes 
a  systematic  presentation  of  their  solution  impossible,  just  as  the 
irregularity  of  conditions  in  any  actual  case  usually  prevents  a 
scientific  solution.  Even  Lehmann-Lenoir,  who  applied  Weber's 
theory,  proceeded  only  by  trial  and  error.^^ 

The  situation  is  somewhat  simpler  when  a  factory  is  to  be  moved 
rather  than  newly  established.  At  any  rate  cost  analysis  offers  the 
lesser  difficulty.  But  how  is  one  to  discover  in  advance  what  demand 
may  be  expected  at  the  various  eligible  locations?'  Here  the  much- 
criticized  "  basing-point  system  "  may  be  an  important  help.  It 
consists  in  charging  the  customer  freight  from  a  point  different  from 
the  point  of  production.  By  considering  one  eligible  location  after 
another  as  a  basing  point,  the  effect  on  demand  will  be  almost  ^^  as 
though  the  industry  had  been  experimentally  established  at  these 
various  places,  while  the  risk  of  actual  investment  is  not  incurred.^'' 

j8.    Special  Location  of  the  Point  of  Greatest  Profit 

In  comparison  with  one-sided  orientation,  an  orientation  by 
profits  could  produce  new  special  locations  at  favored  points  where 
neither  outlay  is  lowest  nor  proceeds  are  highest,  but  where  their 
difference  is  greatest.  There  is,  however,  no  industry  in  which  this 
would  necessarily  be  the  case. 

With  complete  orientation,  production  necessarily  takes  place  at 
a  favored  point  only  when  it  requires  an  irreplaceable  or  immobile 


improbable  can  be  determined  for  different  industries.  Conversely,  it  can  be  stated 
for  individual  locations  whether  they  are  likely  to  attract  industries,  and  which  ones. 
Thus  far,  however,  we  lack  systematic  cost  analyses  for  the  different  industries,  and 
especially  geographic  price  analyses  of  the  individual  cost  factors. 

34.  Our  conclusions  on  the  economic  importance  of  distance  for  the  individual  firm, 
for  example,  on  the  geographic  gradation  of  prices,  and  many  others  are  of  direct 
practical  interest. 

35.  F.  Lehmann-Lenoir,  Les  verreries  suisses.  Etude  comparative  de  leur  repartition 
territorial  efjective  et  de  celle  resultant  de  la  "  Reine  Theorie  des  Standorts  "  d'Alfred 
Weber  (Soleur,  1940) ,  pp.  217  ff. 

36.  In  some  respects,  for  example  where  the  advantages  of  actual  contact  are  con- 
cerned, it  makes  a  difference  whether  the  industry  is  actually  moved  or  not. 

37.  Producers  with  branches  can  establish  new  enterprises  more  easily  than  those 
with  but  one  plant,  since  the  former  can  draw  more  reliable  geographic  comparisons 
from  actual  experience  than  if  they  had  to  rely  on  estimates  alone. 


32 


Part  One.    Location 


production  factor  or  consumer,  or  a  still  rarer  combination  of 
such  factors  or  consumers  (technically  conditioned  special  location) 
whether  at  one  place  (definite  special  location)  or  several  (indefinite 
special  location) .  In  the  latter  instance  the  location  will  be  deter- 
mined by  the  simultaneous  consideration  of  all  the  other  location 
factors,  including  proceeds,  in  contradistinction  to  one-sided  orien- 
tation by  total  costs.  Definite  technically  conditioned  special  loca- 
tions will  necessarily  be  confirmed  by  profit  calculations;  others, 
which  depended  on  one-sided  orientation,  may  be  so  confirmed. 
Should  production  be  carried  on  at  a  special  location  when  only 
proceeds  (a  purely  economic  restriction)  or  transportation  costs  are 
considered,  it  can  always  be  shifted  or  eliminated  by  inequality  in 
production  costs,  and  usually  ^^  by  the  changeability  of  demand  (as 
son  as  the  market  area  is  no  longer  sharply  defined.) 

In  retrospect,  it  is  clear  that  special  locations  are  probably  more 
numerous  with  one-sided  than  with  complete  orientation.  In  reality, 
they  are  therefore  more  significant  than  they  would  be  in  a  rational 
world.  Only  a  few  obvious  and  easily  surveyed  factors  are  generally 
taken  into  account  in  choosing  a  location,  and  often  enough  all  but 
a  single  one  are  eliminated  as  trifling  because  a  real  comparison 
would  be  far  too  difficult.  Thus  it  happens  that  special  locations 
are  more  common  in  reality  than  they  should  rationally  be. 

§3,     Orientation   and   Especially   Favorable 
Locations 

Up  to  now  orientation  has  had  several  meanings  in  the  literature 
of  location.  It  may  mean  the  motives  for  or  the  outcome  of  a  choice 
of  location.  In  the  former  case  it  denotes  the  factors  that  are  taken 
into  account  either  (1)  exclusively  or  (2)  as  especially  important. 
We  have  employed  the  term  only  in  the  sense  of  (1)  :  transport 
orientation,  orientation  by  production  costs,  total  costs,  proceeds, 
and  possibly  by  profits.^^ 

In  the  second  case  one  (3)  describes  or  at  the  same  time  (4)  gives 

38.  If  a  special  location  depends  on  established  lines  of  communication,  demand 
conditions  alone  cannot  as  a  rule  eliminate  it;  if  it  depends  on  weight  ratios,  demand 
conditions  can  ^eliminate  it  only  if  the  finished  product  predominates  (provided  that 
the  tariff  is  not  graduated  and  that  all  costs  imposed  by  distance  except  freight  are 
insignificant) .  This  predominance  may  be  lost  when  the  finished  product  is  shipped 
to  several  places,  so  that  only  the  resultant  of  these  divided  forces  is  operative.  If,  on 
the  other  hand,  a  raw  material  predominates,  nothing  can  alter  this,  no  matter  how 
the  consumers  are  distributed. 

39.  As  well  as   (extra-economically)    by  the  technical  conditions  of  production. 


Industrial  Location  Theory  33 

reasons  for  the  result  of  the  choice.  The  first  of  these  simply  names 
an  actual  situation  at  the  source  of  a  location  factor  after  that  factor, 
but  it  remains  an  open  question  whether  this  factor  is  also  respon- 
sible for  the  choice  (we  shall  call  this  "  situation  "  at  the  source 
of  supply  for  raw  material,  etc.) .  The  second  implies  that  the  factor 
at  whose  location  production  is  situated  has  obviously  caused  the 
choice.  This  explanation  is  meaningful  only  in  the  case  of  technical 
restriction.  It  is  sufficient  for  one,"  and  a  necessary  (though  only 
partial  explanation)  for  several  sources  of  the  same  kind  (it  is  better 
to  speak  of  definite  or  indefinite  "  technical  restriction  "  to  sources 
for  raw  material,  etc.— dj  in  Table  1)  .^^  But  it  may  mean  only  that 
the  actual  site  is  rational  though  not  technically  due  to  the  factor 
located  in  the  same  place.  (We  call  this  either  "  economic  "  or 
"  extra-economic  "  restriction  to  a  point  of  consumption,  etc.— dz 
and  ds  in  Table  l.)*^ 

40.  Apart  from  the  fact  that  whether  or  not  production  will  pay  at  all  depends  also 
on  every  other  factor  influencing  profit.    (See  Predohl,  op.  cit.,  p.  294.) 

41.  As  such  technical  restrictions  are  imposed  mainly  though  not  entirely  by 
nature,  the  influence  of  nature  on  the  choice  of  a  location  may  be  briefly  sketched. 
The  natural  causes  for  local  differences  in  the  economic  scarcity  of  means  of  production 
may  be  divided  into  (1)  their  natural  abundance,  first  as  to  the  number  and  second 
as  to  the  extent  of  their  sources;  and  (2)  their  technical  suitability  for  shipment 
(mobile  or  immobile) . 

According  to  the  number  of  the  sources  of  supply,  production  is:  (1)  With  immobile 
means  of  production  unconditionally  dependent  on  source  technically  and  economically 
(one  source) ;  conditionally  dependent  (several  sources) ;  or  free  to  choose  a  source 
(ubiquity  through  occurrence) .  (2)  All  mobile  means  of  production  allow  technical 
independence  of  their  source,  no  matter  what  the  number  of  their  sources  (ubiquity 
through  transportation) . 

Thus  a  location's  technical  independence  of  its  sources  predominates  except  where 
immobile  factors  of  production  are  found  at  only  one  or  a  few  sites.  Technical  ubiquity 
need  not  be  economic,  however,  and  vice  versa.  A  locally  varying  economic  scarcity  of 
factors  of  production  can  only  limit  still  further  the  possibilities  of  a  production 
location  that  are  already  narrowed  by  technical  scarcity.  It  cannot  extend  them. 

In  addition  to  influencing  the  choice  of  a  location  through  sources  and  the  tech- 
nique of  transportation,  nature  influences  it  through  the  technique  of  production, 
which,  however,  depends  not  solely  upon  nature  but  also  upon  price  relationships. 
Nevertheless,  nature  does  affect  in  this  way  the  kind  and  relative  amounts  to  be 
shipped.    (The  extent  of  the  weight  loss  is  only  one  factor  among  others.) 

42.  It  is  clear  how  protean  the  all-too-popular  concept  of  orientation  is.  When  it  is 
said,  for  example,  that  an  industry  is  "  oriented  to  raw  material,"  does  the  phrase 
mean:  (a)  That  in  choosing  a  location  attention  need  be  paid  to  raw  materials  alone? 
But  to  which  of  several?  To  the  cost  of  its  production  or  of  its  transportation?  To  its 
quality  or  its  quantity?  Or  (b)  that  the  raw  material  merely  plays  the  most  important 
role  among  several  location  factors?  Or  (c)  simply  that  the  production  in  question 
usually  occurs  at  a  source  of  raw  material,  whatever  the  reason?  Or  (d)  do  we  refer  to 
an  industry  that  for  technical  reasons  can  be  carried  on  only  at  this  source?   If  there 


34 


Part  One.     Location 


"  Especially  favorable  location,"  the  situation  of  production  at 
a  favored  site,  is  for  any  particular  type  of  orientation:  (aa)  definite, 
when  only  one,  or  (bb)  indefinite,  when  a  whole  group  of  favored 
sites  could  provide  the  desired  location.   In   (bb)   it  is  certain  only 


Table  7 


Motives  for  Choice  of 
Location 

(a) 

Partial 
(one- 
sided) 

(b) 

All 
factors 

con- 
sidered 

Extra- 
eco- 
nomic 

Orientation 

Result 

of 

choice 

of 

location 

Ordinary  location 

1 

4 

7 

(c) 
Special 
loca- 
tion 

(bb) 
Indefi- 
nite 

— 

— 

8 

Techni- 
cally con-  1 

Expla- 
nation 
of 

special 
loca- 
tion 

(aa) 
Defi- 
nite 

— 

—              9 

sary 

(cc) 
(d,) 

2 

1 
5            — 

i 

Techni- 
cally and 
economi- 
cally 

— 

— 

10 

Techni- 
cally and 
extra-eco- 
nomically 

Fortui- 
tous 
(dd) 

3 

6 

— 

Economi- 
cally  (d2) 

— 

~ 

11 

Extra- 
economi- 
cally  (d3) 

The  letters  refer  to  the  categories  set  up  in  the  text. 

that  there  is  a  special  location;  in  (aa)  the  situation  of  this  special 
location  is  determined.  This  is  (cc)  necessary  when  based  upon  a 
technical  restriction;  (dd)  fortuitous  when  the  restriction  is  only 
economic  or  even  extra-economic.    A  fortuitous  special  location  is 


are  several  raw  materials,  is  "  orientation  to  raw  material "  an  adequate  explanation 
for  any  actual  location?  Or,  finally,  should  a  raw  material  source  happen  to  prove  the 
most  suitable  location  when  several  or  all  factors  are  considered,  is  "  orientation  to 
raw  material  "  only  subsidiary  to  transport  orientation,  orientation  by  production,  or 
complete  orientation?  It  would  obviously  be  better  to  describe  the  situation  in  plain 
words. 


Industrial  Location   TIteory  35 

always  definite  (e.  g.,  transport  orientation)  ;  a  necessary  one  may 
be  indefinite  (as  with  orientation  by  technical  restrictions  on  pro- 
duction) .^3  A  rational  special  location  is  always  definite,  but  a 
definite  one  is  not  always  rational. 

Table  1  shows  the  relation  between  orientation  and  special  loca- 
tion in  their  various  meanings.  One-sided  orientation  need  not  lead 
to  a  special  location  (Space  1) ,  and  special  location  does  not  neces- 
sarily presuppose  one-sided  orientation  (Spaces  5,  6,  8-11).**  "  Tech- 
nical restriction  "  means  in  the  nature  of  things  a  special  location, 
but  this  remains  uncertain  (Space  8)  unless  costs  (Space  2) ,  profits 
(Space  5)  or  extra-economic  considerations  (Space  10)  are  also  taken 
into  acount— with  the  exception  of  an  unavoidable  technical  restric- 
tion at  one  single  source  of  supply  (Space  9) .  In  this  case  only  will 
even  one-sided  orientation  necessarily  provide  a  rational  special 
location,  because  by  way  of  exception  it  is  synonymous  with  orien- 
tation by  profits.  As  a  rule,  however,  no  single  factor  can  indicate 
a  location.  All  influence  it,  many  favor  it,  but  none  determines  it. 
Many  reasons  lie  behind  its  choice.*^*® 


43.  Transport  orientation  is  merely  an  economic  restriction;  orientation  by  pro- 
duction may  be  also  a  technical  restriction. 

44.  For  example,  it  does  not  follow  from  location  in  a  market  area  that  easy  sales 
determined  the  choice  of  this  location  in  whole  or  even  in  part.  In  many  other  cases, 
on  the  contrary,  the  location  of  consumers  has  a  great  influence  on  the  choice  of 
location,  though  it  is  concealed  because  the  resultant  of  the  various  forces  favors 
another  location,  which  appears  to  be  independent  of  consumption. 

45.  The  location  of  any  particular  coal  mine,  for  instance,  cannot  be  fully  explained 
by  the  presence  of  coal.  Only  the  whole  relationship  between  production  and  demand 
that  results  in  profits  will  make  clear  why  coal  is  mined  at  just  this  spot  and  at  no 
others.  Which  of  the  possible  mines  will  actually  be  worked  depends  among  other 
things  on  its  technical  productivity  and  the  local  prices  of  the  factors  of  production 
on  the  one  hand  (cost  curve) ,  and  transport  relations  to  the  market  (demand  curve) 
on  the  other.  Thus,  whereas  over  half  of  the  American  coal  deposits  are  said  to  lie 
in  the  Rocky  Mountains  (Sten  de  Geer,  "  The  American  Manufacturing  Belt,"  Geo- 
grafiska  Annaler,  1927,  pp.  233-359) ,  unlike  the  coal  fields  in  the  Appalachians,  they 
have  not  attracted  many  industries  nor  are  they  worked  to  any  great  extent  because  of 
of  their  unfavorable  location.  Although  coal  is  widely  distributed,  coal  mining  is 
rather  concentrated.  Hence  "  orientation  by  raw  material,"  or  more  exactly  "  restric- 
tion by  raw  material,"  is  not  an  adequate  explanation  here,  where  this  factor  is  only 
one  of  those  taken  into  account.  By  itself,  therefore,  it  is  a  false  explanation  for  the 
special  location. 

46.  The  relation  of  special  location  to  orientation,  even  in  the  meanings  that  we 
do  not  employ,  is  this:  Special  location  is  the  possible  but  not  inevitable  result  of 
orientation  in  the  sense  of  (a)  or  (&)  ;  on  the  contrary,  it  is  the  necessary  condition 
for  orientation  in  the  sense  of   (c)   or   (d)  . 


Chapter  5.      The  Theory  of  Agricultural  Location 


As  far  as  industry  is  concerned,  we  have  discussed  thus  far  only 
the  location  of  an  additional  enterprise.  That  is,  we  have  considered 
the  location  problem  from  the  standpoint  of  the  individual  firm. 
Later  we  shall  describe  in  detail  how  industry  as  a  whole  is  located. 
With  agriculture,  this  more  general  statement  of  the  problem— 
namely,  where  a  particular  product  is  grown— is  of  greater  interest 
from  the  very  first.  At  the  same  time  a  second  important  problem 
is  solved:  what  is  to  be  produced  in  a  particular  place  or  by  what 
particular  enterprise. 

a.     PARTIAL     (ONE-SIDED)    ORIENTATION 

These  problems,  too,  can  be  simplified  by  ignoring  some  of  the 
factors  that  should  properly  be  considered.  Of  the  various  problems, 
the  importance  of  location  has  been  most  thoroughly  examined  (by 
Thiinen) .  Later  we  shall  discuss  changes  in  the  quality  of  the  soil, 
and  in  demand.  When  we  finally  consider  the  remaining  factors, 
especially  joint  demand  and  supply,  local  wage  differences,^  and 
local  variations  in  prices  to  the  enterprise,  we  shall  move  to  an 
orientation  that  takes  all  factors  into  account.  But  here,  too,  as  with 
industrial  location,  we  shall  have  to  forego  a  geometrical  solution. 

§1.     System  Based  on  Thunen's  Theory 

a.    Preliminary  Remarks 

Thiinen  regarded  industrial  locations  as  given,  and  deduced 
agricultural  locations  from  them.  Basically  he  discussed  a  special 
case  of  reactions  to  the  choice  of  the  location  of  an  individual 
enterprise   (Fig.  3) . 

Let  O  be  the  site  of  an  enterprise  that  sells  its  product  in  two 
forms,  one  of  which  is  cheaper  to  produce  per  unit  of  consumption 
while  the  other  is  cheaper  to  ship.  Let  OA  be  the  factory  price 
for  a  machine  and  AB  the  cost  of  knocking  it  down  for  shipment 

1.  G.   Pavlovsky,   Zur  Frage   der   raumlichen   Ordnung   der   Landwirtschaft,   Inter- 
nationale Landwirtscliaftliche  Rundschau,  I,  33    (1942) ,  337-373. 

36 


Agricultural  Location 


37 


and  reassembling  it  at  the  purchaser's.  Transport  cones  are  drawn 
from  A  and  B  that  give  the  c.  i.  f.  prices  for  various  distances.  The 
cone  above  A  is  more  acute  because  it  costs  more  to  ship  a  bulky 
or  delicate  machine  in  assembled  form.  Nevertheless,  up  to  the 
distance  OD  the  delivered  price  is  lower  for  the  assembled  machine, 
and  only  beyond  D  will  it  be  shipped  knocked  down." 

Still  another  situation  is  elucidated  by  Figure  3.  Suppose  that 
different  competing  products  rather  than  different  forms  of  the 
same  product  are  produced  at  O.  Let  the  first  of  these  two  products 
be  cheaper  to  produce  per  unit  of  consumption  but  more  expensive 


Fig.  3. 

to  ship  (low-grade  surface-mined  ore) ;  let  the  other  be  more  expen- 
sive to  produce  but  in  return  cheaper  to  ship  (rich  ore  mined 
underground) .  The  market  area  for  the  poor  ore  will  therefore 
extend  from  the  mine  to  the  distance  OD,  and  only  then  will  the 
ring  be  reached  within  which  it  is  cheaper  to  smelt  the  rich  ore.^ 

Figure  3&  illustrates  similar  cases,  except  that  O  is  now  no  longer 
the  center  of  production,  but  of  consumption,  and  the  rings  around 
O  are  now  conversely  rings  of  different  productions.  Suppose  that  a 
certain  product  raised  in  the  neighborhood  of  O  is  purchased  there 
in  crude  or  finished  condition.  Assume  that  processing  on  the  spot 
is  more  expensive  because  it  must  be  carried  out  on  a  small  scale, 
but  that  it  will  save  freight  charges  because  it  decreases  weight. 
For  example,  let  OA  be  the  price  paid  for  potatoes  by  starch  factories 


2.  Another  example  is  cotton,  which  for  shipment  over  long  distances  requires  the 
additional  process  of  compression  in  large  presses.  Similarly,  with  lignite  the  calorific 
value  and  manufacturing  costs  are  greater  per  unit  of  weight  for  briquettes,  so  that 
these  are  sold  in  a  distant  market. 

3.  If  OA  is  the  low  price  of  electric  current  from  a  large  power  station  erected  in 
a  coal  district,  and  AB  the  loading  costs  of  coal  (i.  e.,  costs  independent  of  distance) 
plus  the  additional  cost  of  small  power  stations,  and  if  the  costs  that  depend  on 
distance  are  lower  for  coal  than  for  electricity,  current  will  be  transmitted  in  the 
vicinity  and  coal  shipped  to  distant  points.  See  C.  Pirath.  Die  Grundlagen  der  Ver- 
kelusu'lrtscliaft    (Berlin,  1934)  ,  pp.  201  ff. 


38  Part  One.     Location 

at  O,  and  AB  the  amount  by  which  the  cost  of  local  reduction  to 
starch  exceeds  that  at  a  center.  The  vertices  of  the  cones  drawn 
from  A  or  B  then  represent  the  grower's  price  for  potatoes  as  a 
function  of  distance.  For  all  farmers  in  the  region  OD  it  will  clearly 
be  more  advantageous  to  ship  potatoes  to  the  town  to  be  worked  up 
at  a  center,  whereas  those  at  a  greater  distance  will  do  better  to 
ship  starch. 

The  same  figure,  Sb,  throws  light  on  still  another  situation, 
which  is  of  special  interest  in  the  present  connection.  Let  O  be  the 
market  for  different  products  rather  than  for  different  forms  of  the 
same  product.  One,  potatoes,  yields  economic  rent  OA  per  hectare 
when  raised  in  the  immediate  vicinity  of  O,  whereas  corn  yields 
only  rent  OB  there.  The  picture  changes  with  increasing  distance 
from  O,  because  a  greater  weight  of  potatoes  than  of  corn  can  be 
harvested  from  a  hectare.  The  freight  charges  for  sending  these 
yields  to  O  will  therefore  be  higher  for  potatoes.  With  increasing 
distance  the  freight  absorbs  the  rent  from  potatoes  more  quickly 
than  that  from  corn,  and  from  the  distance  OD  outward  only  corn 
rather  than  potatoes  will  be  raised.  Thus  cultivation  of  the  various 
crops  is  spread  out  in  rings  around  the  market. 

^.    Possible  Cases 

The  famous  Thiinen  rings  represent  special  cases.  The  reasons 
for  and  the  limitations  of  this  solution  will  be  clearer  when  its 
place  in  a  complete  system  is  seen.  For  this  purpose  the  following 
symbols  have  been  chosen: 

Independent  Variables 

A:  Outlay  per  hectare,  in  marks 

E:  Yield  per  hectare,  in  centners 

p:  Market  price  per  centner 

k:  Distance  from  market,  in  kilometers 

/:  Freight  per  centner  per  kilometer 

Derived  Variables 

A 
a  =  -^ :   Outlay  per  centner,  in  marks 

TT  =  p  —  kf:  Local  price  per  centner 

r  ^ir  —  a:  Local  profit  per  centner 
R  =  rE  =  E  {p  —  kf)  —A:  Rent  per  hectare 
m  ^  p  —  a:  Highest  profit  per  centner 

(==  highest  freight  possible  without  loss  to  producer) 


Agricultural  Location 


39 


Table  2.   COMPLETE  SYSTEM  OF   SPATIAL   ORDER   IN 
AGRICULTURE  FOR  TWO   CROPS 


Variables  Fulfill  Condition 

1 

Relative 

No.  (m) 

Crop  Produced 

1        2 

1    1    2 

1 

2 

Monoculture 

Polyculture 

i"^ 

Size 
of 

o  c 
^•2 

Conditional 

Variables 

Some- 

Uncon- 

a 
o 

^■■v 

Always 

times 

Never 

ditioned 

a 

Culti- 

6 

vated 

Rings 

6 

together 

E, 

Ai 

Pi 

I 

I  and  II 

I 

II 

V 

to 

to 

to 

I 

II 

or 

side  by 

in- 

in- 

u 

Eo 

A^ 

P2 

II 

side 

side  i  side  1 

1 

> 

X 

X 

0 

0 

1 

2 

> 

= 

X 

X 

0 

0 

3 
4 

< 

X 

X 

0 

. 

0 

> 

X 

X 

0 

5 

> 

= 

= 

X 

X 

0 

6 

7 

< 

X 

X 

0 

0 

> 

X 

• 

X 

0 

8 

< 

= 

X 

X 

0 

9 
10 

< 

X 

X 

0 

0 

> 

X 

X 

0 

0 

11 

> 

= 

X 

X 

0 

12 
13 

< 

X 

X 

0 

> 

X 

X 

0 

^ 

14 

= 

= 

= 

X 

X 

. 

0 

15 
16 

< 

X 

X 

0 

> 

X 

X 

0 

17 

< 

= 

X 

X 

0 

18 

< 

X 

X 

0 

0 

19 

> 

X 

X 

0 

0 

20 

> 

= 

X 

X 

0 

21 
22 

< 

X 

X 

0 

> 

X 

X 

0 

0 

23 

< 

= 

= 

X 

X 

0 

24 

< 

X 

X 

0 

25 

> 

X 

X 

0 

0 

26 

< 

= 

X 

X 

0 

0 

27 

< 

X 

X 

0 

0 

(m)     See  text  for  definition  of  conditions,  p.  40. 


40 


Part  One.     Location 


Table  2  contains  all  possible  variations  of  the  relative  magni- 
tudes of  the  first  three  independent  variables  for  two  crops,  I  and  II. 

y.    Spatial  Order 

We  seek  those  cases  where  both  crops  are  raised.  Only  then 
does  the  problem  of  their  spatial  order  arise.  Both  crops  will  be 
grown  when  one  yields  a  gieater  rent  per  hectare  at  the  center 
of  the  area  and  the  other  at  its  periphery.  The  condition  under 
which  I  will  yield  a  greater  rent  at  the  center  than  II  is  Ri  >  R.. 
This  yields: 

First  Condition:   1  <  ^^'^^~^^  (I)  * 

The  condition  under  which  II  will  yield  a  greater  rent  at  the 
periphery  is:  Ri  <  R2.    This  gives 

Second  Condition:  ^''t'~'l'  <  |^  (2) « 

E2-p2—A2  £2 

4.  This  is  derived  as  follows: 

R^  >R,. 
substituting 

E^-{p,-kf)  -A,>E,-(p,-kf)  -A^. 

Since  at  the  center  of  production  k  =  0,  this  becomes 

Ei-pi-A:,>E2-p2-  A^. 
By  dividing  this  becomes 

Ez'  p2—  A2 

5.  This  is  derived  as  follows: 

Ri  <  R2. 
By  substitution  we  get 

E^-  (p.-kf)  -A^<E^-{p^-kf)  -A- 
But  at  the  periphery 

Therefore 

^1  •  (Pi  —  p2  +  ao)  -Ai<E2  {p2  -p2  +  a^)  -  ^2 
£ipi  —  £1^2  +  fiifla  —  ^1  <  £2^2  —  ^2^2  +  Em„  —  A^. 

Simplifying  and  substituting  a^  ^=  — ?,  we  get: 

E2 

E,pr  -  E,p,  +  ^  -  ^,  <  E,p,  -  E,p,  +  -J^  -  A, 

E^p^-E,p,+  -^-A^<0 

7-2         A    ^  T?  I,       E^Az       EJEspz  —EiAz       El 

E^pr  -A^<  E^p.  -  ——  = i— ==  —  {E2P2  -  A2) . 

£,2  £,2  £.2 

Dividing  by    {E.p.  —  A.)    we  get 


E.p,-A,  ^Ei  j3 

E2P2  —  Aj        £3 


Agricultural  Locution  <jl 

Both  conditions  combined: 

'^E,p,-A,^E,  ^^^ 

First  we  establish  for  what  variations  oi  A,  E,  and  p  conditions 

(1)   and  (2)  are  fulfilled.   Table  2  shows  that  of  27  cases  condition 

(1)    alone  is  always  fulfilled  in  7,  and  that  condition    (2)    alone  is 

always  fulfilled  in  7  further  cases.    In  the  first  7  the  cultivation  of 

crop  II  will  nowhere  be  advantageous;  in  the  other  7  only  crop  II 

will  be  grown. 

In  12  additional  cases  our  assumption  on  the  relative  magnitudes 
oi  A,  E,  and  p  is  not  sufficient  to  decide  between  the  different  crops. 
They  leave  it  open  whether  only  one  or  both  together  will  be 
planted.  The  latter  will  occur  either  when  both  conditions  are 
fulfilled  or  when  neither  is.  This  depends  on  the  exact  numerical 
value  of  ^,  £,  and  p.  If  both  conditions  are  fulfilled  or  if  neither 
one  is,  cases  10  and  18  differ  from  the  remaining  10.  Since  in  both 
cases  Ex/E^=  1,  both  conditions  can  never  be  met.  On  the  other 
hand,  it  has  the  same  effect  that  for  (pi  —  p^  =  (a^  —  do)  both 
conditions  are  unfulfilled  at  the  same  time.^  The  cultivation  of 
both  crops  simultaneously  is  then  possible  as  in  the  other  10  cases. 
They  can  even  be  grown  side  by  side  in  adjoining  sectors  within 
the  same  ring  instead  of  in  successive  rings  only,  as  in  the  other 
10  cases. 

For  the  remaining  10  cases  certain  relative  values  for  A,  E,  and 
p  exist  for  which  both  conditions  are  fulfilled.  The  choice  of  a 
crop  is  then  a  function  of  distance.  In  all  cases  where  Ex  >  Ez 
crop  I  will  necessarily  be  grown  in  the  inner  ring.  In  all  cases 
where  Ex  <  £2  it  will  just  as  necessarily  be  grown  in  the  outer  ring. 
If  £1  =  Eo,  only  one  of  the  crops  in  question  can  be  grown  eco- 

6.  To  prove  that  when    (pi  —  pz)  =  (a^-a^)    neither  condition    (1)    nor  condition 
(2)   can  be  fulfilled: 

£,1         £,2 

If  £1  =  £2.  as  assumed  in  cases  10  to  18,  it  follows  that 

Ei{pi  —  p2)  =A^  —  A^;    therefore  E^p^  — Ai  =  E^p^  — A^. 
Dividing  by  the  right  side: 

Eipi  —  ^2 
But  condition    (1)    requires  that  this  expression  be  greater  than  unity;  condition    ^2) 
requires  that  it  be  smaller  than  unity.— \V.  F.  S. 


42 


Part  One.     Location 


nomically  as  a  rule,  with  the  following  three  exceptions:  in  cases 
10  and  18,  already  mentioned,  it  is  possible  under  certain  conditions, 
and  in  case  14,  the  median  case  of  the  whole  system,  it  is  always 
possible,  to  plant  both  crops  side  by  side.  We  shall  now  examine 
more  closely  those  10  of  the  27  cases  in  which  rings  may  be  formed. 

8.    Reason  for  the  Formation  of  Rings 

1.  More  Exact  Reasons.  For  the  choice  of  a  crop  to  depend 
upon  distance,  conditions  (1)  and  (2)  must  be  simultaneously 
fulfilled.  When  crop  I  should  be  grown  in  the  inner  ring,  equation 
(3)   shows  that  the  following  must  be  true:  ^ 

£2  {p2  —  a^)  <  £1  {pi  —  a,)  <  £1  {p2  —  fla) 
or 

£2^22  <  ^iW^i  <  -£1^12         or         jEimi  >  £2^2 

Since  m^  <  mg,  it  follows  that  Ei  >  £2- 

Thus  crop  I  brings  in  the  greater  total  profit  {Ej_mi) ,  but  the 
smaller  profit  per  unit  (mi) .  From  this  it  follows  that  the  physical 
yield  £1  per  unit  of  area  is  greater.®  The  first  inequality  makes  it 
certain  that  crop  I  is  superior  at  the  market;  the  second,  that  it  is 
superior  only  there.  If  both  inequalities  are  fulfilled— that  is,  if 
rings  are  established  at  all— the  product  with  the  greater  return  by 
weight  will  be  cultivated  in  the  inner  ring.®  The  exact  reason  why 
the  superiority  of  crop  I  is  lost  with  distance  from  the  market  is 
that  freight  charges  absorb  its  unit  profit  more  quickly,^"  until  a 


(3) 


7.  Derived  as  follows: 

E2P2  —  A  2       E2 
since  a  =  A/E,  A  =  aE;  substituting  in    (3) , 
J       £ipi  -  aiEi       E^ 

J  ^  E^(pi-aj)        E^^ 

£2  (p2  -  «2)  £2  * 

Multiplying  through  and  simplifying: 

£2(^2-0.)  <£i(pi-ai)  <  £1(^2-^2)         Q.E.D. 

8.  Geometrically  this  means  (in  the  same  order)  that  in  Figure  7a  /  cuts  the 
M-axis  farther  from,  the  distance  axis  nearer  to,  the  origin,  and  hence  is  steeper  than 
II.  The  point  of  intersection  with  the  /cm-axis  marks  the  greatest  possible  distance 
for  shipment   (m/f)  ,  which  for  crop  I  is  smaller. 

9.  This  is  neither  an  additional  nor  a  sufficient  condition  for  ring  formation,  but 
a  necessary  one  (though  it  is  already  contained  in  the  two  others)  .  It  cannot,  there- 
fore, replace  either  of  these. 

10.  A  more  detailed  analysis  would  have  to  take  into  account  that  the  price  of  the 


Asricultiiral  Location  43 

point  is  arrived  at  where  this  is  no  longer  outweighed  by  the  gi  eater 
yield  per  hectare:  the  boundary  line  between  the  two  crops  has 
been  reached.^^ 


same  physical  input  also  varies  with  distance  and  with  the  possible  freight.    Near  a 
town,   labor  especially   becomes   more   expensive   and   agricultural   machines   cheaper. 

Let  us  sketch  at  least  briefly  the  manner  in  which  nominal  agricultural  wages 
depend  on  distance  from  the  market.  Suppose  that  the  amounts  in  the  laborer's 
budget  are  independent  of  price;  that  agricultural  and  industrial  commodities  can  be 
combined  into  a  general  commodity  of  which  the  amounts  /  and  i  are  supposed  to  be 
consumed  per  year.  Let  /  be  the  freight  per  unit  of  quantity  and  distance,  and  pi 
or  pi  the  unit  price  in  the  town;  suppose  finally  that  the  real  wage  is  the  same 
everywhere   (/J  =  /  +  »  =  a  constant) . 

How  does  the  nominal  wage  (Na)  vary  with  the  distance  (a)  ?  The  nominal  wage 
equals  quantity  times  the  price  of  agricultural  and  industrial  goods: 
Na  =  l(p,-af)  +  i{pi  -\- af)  =  Ip,  +  ipi  +  af{i~l)  . 
Of  these,  Ipi  and  ipi  are  constants,  whereas  af{i—l)  depends  on  distance.  Whether 
the  nominal  wage  will  decrease  or  increase  with  distance  from  the  town  will  therefore 
depend  upon  whether  a  greater  weight  of  agricultural  or  of  industrial  goods  is 
consumed. 

Even  today  agricultural  goods  are  likely  to  preponderate.  The  urban  annual  con- 
sumption per  capita  is  roughly  500  kg.  of  food  and  400  kg.  of  coal.  The  rural  laborer 
receives  by  way  of  the  town  perhaps  60  kg.  of  industrial  goods  and  80  kg.  of  food  (in 
the  country  potatoes,  milk,  flour,  and  meat  make  up  three  fourths  of  all  foodstuffs) . 
He  uses  less  coal  than  the  town  dweller  because  he  burns  wood,  and  besides  coal  does 
not  always  reach  the  country  from  a  town.  Thus  one  can  count  on  only  about  140  kg. 
of  urban  products  as  against  420  kg.  of  rural  products.    Much  depends  upon  fuel. 

A  second  reason  why  agricultural  wages  decrease  with  distance  from  a  town  is  that 
house  rents  are  lower  because  the  ground  itself  is  cheaper  (as  a  result  of  the  small 
agricultural  rent  and  lower  density  of  population)  and  because  natural  building 
materials,  being  nearer,  are  less  expensive.  A  third  reason  is  the  greater  surplus 
population,  which  often  increases  with  distance  from  the  town,  together  with  the 
incomplete  mobility  of  this  surplus.  Fourth,  the  agricultural  laborer  saves  transport 
cost  and  local  taxes,  since  local  services  can  safely  be  lower.  In  the  fifth  place,  he  has 
more  incidental  and  intangible  income  (land  for  gardening,  the  possibility  of  breeding 
small  animals,  and  a  more  natural  way  of  life) .  Sixth,  he  buys  some  things  from 
farmers  at  lower  cost.  Finally,  agricultural  wages,  lowered  for  the  reasons  just  cited, 
are  reciprocally  depressed  still  further  to  a  certain  degree  (by  lower  trade  margins, 
for  example) .  On  the  other  hand,  the  migration  of  the  abler  inhabitants  to  towns, 
where  they  can  specialize  according  to  their  particular  gifts,  does  not  explain  a  real 
difference  in  eSiciency  wages  as  between  town  and  country,  though  it  does  explain  such 
a  differential  among  country  dwellers  in  favor  of  the  skilled  trades. 

11.  The  matter  can  be  expressed  this  way  also:  The  total  freight  is  proportional 
to  the  physical  yield,  but  total  gross  profit  (money  receipts  less  cost  of  production) 
for  crop  I  is  less  than  proportional  to  the  physical  yield,  since  nii  <  rrig.  In  other 
words:  The  gross  profit  on  crop  I  is  greater  than  that  on  crop  II  by  a  smaller  per- 
centage than  its  physical  yield,  which  influences  the  cost  of  transportation.  Hence 
for  the  same  distance  the  latter  makes  up  a  greater  percentage  of  the  gross  profit  for 
crop  I,  and  this  difference  in  percentages  increases  with  distance.  The  originality 
greater  net  profit  for  I,  therefore,  shrinks  more  quickly  with  increasing  freight  costs„ 
and  finally  drops  below  that  for  crop  II. 


44  Part  One.    Location 

2.    Determination  of  the  Transition.    At  the  limit  i?i  =«=  R2,  or 
E^{py-kf)  -A^^E^ip^-kf)  -A2.    Hence 

E,p,-E,p^-\-A,-A,^ 
^-  f(E,-E,) 

or 


_  1  /E^mx  —  EomzY 


The  distance  k  of  the  transition  from  the  center  is  directly  propor- 
tional to  the  difference  in  gross  profits  before  deduction  of  freight 
charges,  and  inversely  proportional  to  the  freight  rate  and  the 
difference  in  physical  yield.    If  the  equation  is  written  as 

kf  =  {E^m^  —  £2^2)  /  (£1  —  E2) 

the  left  side  corresponds  to  the  marginal  cost  (in  freight)  and  the 
right  to  the  marginal  receipts  (over  and  above  production  costs) 
per  centner  Thus  every  production  spreads  out  until  at  the  edge 
of  its  ring  the  rising  marginal  cost  curve  intersects  the  marginal 
revenue  curve. 

This  differs  from  the  usual  discussion  of  marginal  adjustments 
of  an  individual  firm  only  in  that  in  the  latter  case  marginal  cost 
refers  to  production,  whereas  here  it  refers  to  transport  cost.  The 
two  problems  of  the  amount  and  the  location  of  production  are 
thereby  solved  simultaneously.  If  rings  I  and  II  represent  areas  of 
intensive  and  extensive  cultivation  of  the  same  commodity,  between 
which  no  transition  is  possible,  the  difference  from  the  usual  dis- 
cussion of  marginal  adjustments  consists  only  in  the  fact  that  here, 
with  increasing  distance,  the  marginal  cost  for  a  great  part  of  the 
product  (namely,  that  by  which  I  is  more  intensive  than  II) 
suddenly  rises  above  marginal  revenue.  This  leads  to  an  abrupt 
transition  to  extensive  cultivation. 

12.  This  is  reached  as  follows: 

£2^2  -  £ipi  +  A^-A^ 


as  a  -—  A/E,  A  =  aE;   therefore 

ft  _  :^2p2  ~  -^iPi  +  '^i^i  ~  '^^^ 


f{E,-E,) 
I    E^ip.—  a^)  -E^{pi-a^) 


f  E,-E, 

substitiiting   m  =  (p  ~  a) ,    and   multiplying   numerator   and   denominator    by    (—  1)  , 
we  get 

ft  =  1   .  (E.m,-E.mA  q  ^  p  _^  P  S. 

/      \Ei  —  Et      / 


Agricultural  Location 


45 


3.  Popular  Reasons.  The  sequence  of  spatial  order  is  often 
explained  plausibly  and  on  a  common-sense  basis,  even  by  Thiinen," 
by  saying  that  the  "  lighter  "  or  the  "  dearer  "  good  is  produced 
farther  out,  because  with  it  freight  is  less  important."  If  this  vague 
formulation  means  the  commodity  that  costs  more  per  pound,  that 
is,  of  which  fewer  pounds  can  be  bought  for  one  mark,  the  state- 
ment is  false.    In  case   1   of  Table   2,   for  example,   the  cheaper 


I.  Cheap  Product 


II.  Dear  Product 


Fig.  4.    Effect  of  increased  freight  on  the 

demand  for  a  cheap  and  for  an 

expensive  product 

commodity  is  cultivated  on  the  outside.^^  It  is  sometimes  said,  also, 
that  the  more  extensively  grown  crop  comes  from  outside.  This  is 
true  if  only  the  smaller  physical  yield  per  hectare  ^^  is  meant,  inde- 
pendent of  outlay.    This  condition  is  in   fact  necessary  but  not 


13.  H.  V.  Thiinen,  Der  Isolirte  Staat  in  Beziehung  auf  Landwirtschajt  und 
Nationalokonomie    (Wantig  edition,  Jena,  1921) ,  p.  12. 

14.  The  assertion  that  the  more  expensive  commodity  can  "  bear  more  freight "  is 
manifestly  incorrect  in  this  general  form.  If  N  in  Figure  4  is  the  demand  curve  and  a 
the  cost  of  production,  the  same  freight,  kf,  reduces  the  demand  for  the  more  expensive 
commodity   (II)    to  almost  nothing,  whereas  it  hardly  affects  that  for  the  cheaper  one 

(I) .  Naturally,  with  a  differently  shaped  demand  curve  the  situation  may  be  reversed. 
See  O.  Englander,  "  Emil  Sax'  Verkehrsmittel  und  die  Lehre  vom  Verkehr,"  Schmollers 
Jahrbuch,  1924,  pp.  265-305.  "  The  transportability  of  goods  does  not  depend  on 
their  value  "   {ibid.,  p.  276) . 

15.  Example:  Corn  is  grown  near  the  River  Plate  and  wheat  farther  away,  not 
because  the  latter  is  dearer  but  because  its  yield  per  hectare  with  an  appropriately 
intensive  cultivation  is  smaller  (contrary  to  the  otherwise  excellent  discussion  by  A. 
Riihl,  Das  Standortproblem  in  der  Landwirtschaftsgeographie  [Berlin,  1929],  p.  120). 

The  specific  gravity  of  goods  is  of  as  little  import  as  their  value;  only  the  yield 
by  weight  of  each  unit  of  area  is  decisive.  On  a  par  with  it  are  higher  freight  rates, 
easy  spoilage,  or  transportation  of  food  or  manure  through  and  beyond  the  town 
(transportation  in  an  opposite  direction) . 

16.  Or,  which  amounts  to  the  same  thing,  reduction  by  drying,  cleaning,  butchering, 
and  so  on.    In  wartime,  when  transportation  is  difficult,  this  concentration  is  carried 


^6  Part  One.     Location 

sufficient,  since  it  is  still  possible  that  the  extensive  or  intensive 
crop  will  be  cultivated  everywhere.  But  if  "  extensive "  means 
"  smaller  outlay  per  unit  of  area  or  of  weight,"  this  statement,  too, 
is  false.  For  example,  in  case  9  both  are  greater  for  the  product 
cultivated  in  the  outer  ring. 

c    An  Example  of  ThiXnen  Rings 

The  popular  example  of  ring  formation  in  the  sale  of  milk 
may  serve  as  an  illustration  of  the  subject  now  under  discussion.^^ 
When  we  arrange  the  possible  products  in  the  order  milk  (I) ,  cream 
(II) ,  and  butter  (III) ,  it  is  immediately  known  that  the  yield  per 
acre,  E,  falls  in  that  order,  whereas  the  outlay  per  acre,  A,  and 
market  price,  p,  rise.    This  is  case  9  in  Table  2,  and  it  will  be 

very   far   in   areas   that   are   distant   from   their   markets,   so    that   a   relatively   small 
shipping  space  can  transport  the  same  useful  load. 

Weight  is  decreased  by:  (1)  Eliminating  everything  superfluous  or  less  important; 
e.  g.,  shipping  powdered  instead  of  fluid  milk;  fruit  juices  instead  of  fruit;  with  rising 
freight  rates  frozen  meat  rather  than  iced,  then  meat  with  bones  removed,  later  canned, 
finally  dried,  until  at  last  perhaps  only  hides  are  shipped.  (2)  Further  processing 
(bacon  instead  of  corn;  dried  eggs  instead  of  barley;  butter  fat  instead  of  oil  crops) . 
Volume  can  be  decreased  by  compression  also. 

This  diminution  in  the  bulk  of  the  same  commodity  in  areas  far  removed  from 
their  markets  is,  as  Englander  rightly  said  [Theorie  des  Giiterverkehrs  und  der  Fracht- 
sdtze  [Jena,  1924],  p.  118),  only  a  special  case  of  decrease  of  the  yield  in  weight  per 
unit  of  area  away  from  the  market,  except  that  the  one  case  concerns  different  kinds 
ri  commodities  and  the  other  concerns  different  forms  of  the  same  commodity. 
Furthermore,  greater  durability  or  ease  of  handling  is  equivalent  to  a  smaller  yield 
per  hectare  in  lowering  the  freight.  A.  Petersen  (Die  fundamentale  Standortlehre 
Thiinens,  wie  sie  bisher  als  Intensitdtslehre  missverstanden  wurde  und  was  sie  wirk- 
lich  besagt  [Jena,  1936],  p.  16)  correctly  deduces  from  this  that  certain  refining  enter- 
prises (such  as  distilleries,  dairies,  sugar  refineries,  plants  for  the  manufacture  of  starch 
and  the  preserving  and  canning  of  food,  and  grain  mills)  may  have  a  wholly  rational 
location  in  East  Prussia,  though  they  are  far  from  their  markets.  He  errs,  however,  in 
believing  that  the  compatibility  of  such  intensity  at  a  distance  from  the  market  with 
the  Thiinen  theory  had  been  overlooked  until  then.  Adam  Smith  had  already  shown 
that  the  two-fold  freight  charge  causing  low  agricultural  and  high  industrial  prices 
is  conducive  to  industrial  development  in  remote  areas.  The  industries  employ  the 
heavy  products  of  the  soil  cheaply  on  the  spot  and  in  return  ship  a  smaller  weight  in 
low-quality  goods  to  markets  nearby,  and  a  smaller  weight  in  high  quality  goods  to 
more  distant  markets.  {An  Inquiry  into  the  Nature  and  the  Causes  of  the  Wealth  of 
Nations  [London,  "1811],  Book  3,  end  of  Chapter  3,  where  also  there  are  interesting 
observations  on  the  dynamics  of  location.)  A  large  increase  in  population  strengthens, 
whereas  the  scarcity  of  capital  associated  therewith  checks,  this  tendency  toward 
industrialization.  Example:  Balkan  States  (see  A.  Losch,  Was  ist  vom  Geburten- 
riickgang  zu  halten?  [Heidenheim,  1932])  . 

17.  Here   we   may   proceed   as   though   milk,   cream,   and   butter   were   completely 
separate  products. 


AgiicnUural  l.ocaliun  47 

realized  from  the  preceding  analysis  that  it  does  not  necessarily 
lead  to  the  formation  of  rings.  It  is,  on  the  contrary,  possible  that 
one  or  two  of  the  products  are  not  provided  at  all.  We  know, 
further,  that  if  rings  are  formed  the  sequence  of  the  products  cannot 
be  changed.  If  with  a  certain  distance  from  the  market  it  is  more 
profitable  to  make  butter  than  to  supply  milk,^^  but  if  at  the  same 
time  it  is  always  less  advantageous  than  to  separate  cream,"  butter 
making  can  evidently  not  be  spatially  inserted  between  milk  and 
cream  but  must  cease  entirely.  The  inner  product  must  necessarily 
show  the  greater  physical  yield  per  acre. 

Example:  ^° 

E  A  p 

Yield  per  hectare  Outlay  per  hectare  Market  price 
(kg.)                      (pfennigs)  (pfennigs) 

I     Milk  25  250  20 

II     Cream  2.5  300  160 

III     Butter  1  350  380 

Freight  per  kg.  and  km.:  0.10  pfennig 

a  =  A/E 
hence 

fl,  =  10;         a2=I20;         As  =  350 

m==  p  —  a 
hence 

mi  ==  10;         ma  ^  40;  mg  =  30 

Conditions  for  ring  establishment  ^^  between 

I  and  II:  E^m^  <  E,m,  <  E,m.;    100  <  250  <  1000:  Fulfilled 
I  and  III:  E.nis  <  E,m,  <  E^iris;     30  <  250  <  750:  Fulfilled 
II  and  III:  E^m^  <  E^m^  <  E.m^;     30  <  100  >  75:   Not  met  * 
*  II  is  always  more  advantageous  than  III. 

18.  The  producer  of  milk  who  is  near  his  market  has  a  good  location,  not  merely 
because  of  the  difficulties  of  shipment  but  mainly  because  of  the  high  yield  per  acre 

(in  Germany  the  marketable  surplus  of  milk  in  weight  is  greater  than  that  of  grains) . 
This  yield  by  weight  in  sheep  breeding  is  hardly  1  per  cent,  so  that  it  pays  only  on 
very  poor  soil. 

19.  This  is  necessarily  the  case  when  m^  >  mg,  even  though  butter  is  the  "  lighter  " 
and  "  dearer  "  commodity. 

20.  See  also  E.  M.  Hoover,  Location  Theory  and  the  Shoe  and  Leather  Industries 
(Cambridge,  Mass.,  1937)  ,  pp.  30-33. 

21.  See  above,  pp.  40  f.,  where  this  inequality  has  been  developed.— W.  H.  W. 


Part  One.     Location 


Boundary  line  between  I  and  III  at  kilometers 

250  -  30 


/V     E,-E,      )-0.\ 


24 


=  92 


But  at  92  km,  the  rent  from  II  is  already  greater  than  that 
from  III.^^  Thus  butter  making  is  never  started.  To  make  it  pos- 
sible, mg  must  rise  above  rriz.  This  will  happen  as  soon  as  the  butter 
shortage  raises  its  price  to  at  least  400  pfennigs.  Then  rriz  ==  50, 
whereas  mg  is  only  40.    Now  butter  will  be  produced  rather  than 

cream  at  distance  k  = -— f ^-^ — j=  333  km.   With  a  sufficiently 

pressing  demand  such  a  price  change  can  provide  relief  in  those 
cases  where  the  production  of  a  commodity  seems  impossible.  For 
example,  in  case  4  of  Table  2  only  commodity  I  can  be  produced, 
not  commodity  II.  If  the  price  of  commodity  II  were  to  rise  as  a 
result,  and  if  the  urgency  of  the  demand  should  drive  its  price 
above  that  of  commodity  I,  the  situation  obtaining  for  case  4  would 
change  to  that  for  case  6,  where  the  simultaneous  production  of 
both  commodities  is  possible. 

t,.    Interregional  Trade 

Of  course  this  relative  change  in  prices  does  not  always  occur. 
It  may  be  defeated  by  the  shape  of  the  demand  curve,  or  by  out- 
side influences.  If  imports,  for  instance,  prevent  the  price  of  butter 
from  rising,  the  production  of  domestic  butter  will  be  impossible. 
The  single  broken  line  in  Figure  5  shows  the  rent  from  butter 
when  the  price  is  depressed  in  this  way;  it  falls  to  zero  (with  dis- 
tance) before  intersecting  the  more  rapidly  decreasing  rent  on 
cream.  On  the  other  hand,  as  is  easily  seen,  a  slight  decrease  in 
price  caused  by  imports  is  enough  to  push  the  rent  on  cream  below 
the  line  of  dots  and  dashes  and,  unless  butter  is  also  imported,  to 
exclude  the  domestic  production  of  cream  thereby.  The  butter 
ring  then  borders  directly  on  the  milk  ring. 

A  threat  to  the  cream  and  milk  rings  by  competition  from 
another  economic  region  is  much  more  improbable,  of  course,  than 
exclusion  of  the  butter  ring.  Then  the  paradox  arises  that  as  soon 
as  foreign  competition,  through  a  lowering  of  costs,  say,  is  able  to 
send  in  not  only  butter  but  also  cream,  and  perhaps  even  milk,  the 
situation  of  the  domestic  butter  industry  improves  again.  The 
area  of  domestic  production  is  reduced  as  a  whole,  to  be  sure,  but 
if  the  rent  from  cream  should  be  lowered  too  it  may  very  well  fall 

22.  i?,  >  i?3;  E,  (p,  -  92/)  -A,>E,  (p,  -  92/)  -  A^ 
77>21. 


Agricultin-al  Location  49 

again  somewhere  below  the  previously  reduced  rent  on  butter   (as 

in  B'  under ) .  Assume  that  somewhere  abroad  there 

is  an  '  island  "  where  production  costs  are  only  half  as  much  and, 
when  freight  is  neglected  and  with  the  prices  prevailing  at  O,  permit 
a  gross  profit  two  and  a  half  times  as  great  as  that  in  the  domestic 
area  of  supply.  Then  suitable  rings  can  be  established  around  O 
whose  radii,  of  course,  will  be  two  and  a  half  times  as  long.  Now 
imagine  the  "  island  "  of  cheap  production  costs  to  be  moved  slowly 
from  far  away  toward  the  market;  at  first  it  will  not  be  able  to 
compete  despite  its  own  low  costs,  because  of  high  freight  rates. 

M 


"^^Xi^.'^ 

h 

\ 

\ 

miles 

Domestic 


Cream  [     Bulterarea 
L* — .-i-« 

t^ Foreign     — 


Fig.  5.    Rent  per  acre  as  a  function  of  distance 

tg  a:  freight  per  mile  on  the  physical  yield  per  acre 

Moved  farther  inward  toward  the  market,  this  area  reaches  first 
the  butter  ring,  and  in  order  to  compete  in  cream  and  fresh  milk 
too  it  must  approach  very  close  to  the  market.  That  is  to  say,  the 
goods  enter  interregional  trade  in  the  sequence  in  which  they  were 
prepared  far  away  for  the  market."^  If  this  sequence  is  different  in 
the  importing  and  the  exporting  country,  that  of  the  latter  will 
prevail  under  similar  freight  rates. 


23.  For  example,  the  quantities  of  Canadian  exports  to  the  United  States  increase 
in  the  following  order:  fresh  milk,  cream,  butter,  and  cheese. 


50 


Part  One.     Location 


rf.    The  Spatial  Order  of  Production  Systems 

What  we  have  found  for  various  lines  of  production  can  be 
employed  also  for  various  degrees  of  intensity  of  cultivation  of  the 
same  commodity,  in  the  nine  cases  where  pi  =  p2-^^'^^  There  is  a 
boundary  line,  of  course,  only  when  no  gradual  transition  between 
intensive  and  extensive  cultivation  exists.  This  holds,  also,  when  I 
and  II  each  represent  a  whole  assortment  of  commodities;  that  is,  if 
they  represent  a  production  system,  if  only  these  commodities  are 
actually  cultivated  in  both  systems,  even  though  in  different  propor- 
tions and  with  different  intensity.-^  As  soon  as  there  are  transitions 
between  these  proportions  and  these  degrees  of  intensity,  however, 


Coslper  acre 
Fig.  6.    Intersection  of  two  profitability  planes 

the  spatial  boundary  lines  between  the  systems  disappear.  But  if 
I  and  II  stand  for  different  branches  of  agriculture  (i.  e.,  different 
commodities) ,  there  is  a  clear  demarcation  even  when  both  have 
variable  degrees  of  intensity  (Fig.  6) .  Since  every  commodity  can 
be  cultivated  as  a  rule  with  any  desired  variations  in  intensity, 


24.  Here  we  can  equate  the  inner  ring  to  intensive,  and  the  outer  rings  to  extensive, 
cultivation  (in  any  one  of  the  meanings  previously  mentioned),  since  case  2  and  case  26 
are  the  only  ones  among  those  permitting  the  formation  of  rings  in  which  pi  =  p^. 
In  both  cases  the  outlay  and  the  yield  per  hectare  are  gieater  in  the  irtner  ring,  and 
a  moment's  thought  will  show  that  rings  can  be  formed  only  (in  place  of  the 
alternatives  that  only  commodity  I  or  commodity  II  is  cultivated)  if,  for  case  2, 
E1/E2  <  A1/A2,  that  is,  if  intensity  is  maintained  with  diminishing  returns  (if  the 
returns  decrease  greatly,  of  course,  only  II  may  be  cultivated)  .  In  any  case  a^  >  aal 
thus  the  second  criterion  of  intensity  given  on  p.  40  is  fulfilled  too. 

25.  An  example:  Thiinen  found  rotation  of  crops  {K)  in  the  vicinity  of  a  market 
more  advantageous  than  the  three-fallow  system    (D) .    Thus  his  numerical  example 


Agricultural  Location  5^ 

Thiinen  rings  are  subject  to  the  further  restriction  that  in  general 
they  appear  only  with  different  commodities. 

0.    Several  Centers  of  Consumption 

When  production  is  not  grouped  about  one  center  of  consump- 
tion as  has  been  assumed  up  to  now,  but  about  several,  these  select 
their  own  sources  of  supply  from  the  environment  of  the  foremost 
producer  if  they  are  near  enough  (see  Fig.  45)  .  The  rings  under 
discussion  form  around  each  new  center,  but  in  a  region  of  many 
towns  there  is  no  room  for  the  outer  ones;  they  are  displaced 
toward  its  margin.  The  number  of  displaced  rings  increases  with 
the  density  of  towns.  For  the  inner  rings  the  individual  town  is 
the  marketing  center,  for  the  outer  ones  the  agglomeration  of  towns. 
Thus  with  the  growth  of  northwestern  Europe  more  and  more 
branches  of  agriculture  with  a  low  yield  per  acre,  such  as  sheep 
breeding,  grain  growing,  and  the  production  of  some  feeds,  of  butter 
and  of  cheese,  moved  overseas  and  to  eastern  Europe.-®  This  develop- 
ment, first  described  in  detail  by  H.  Engelbrecht,^^  has  been  discussed 
recently  by  H.  Backe.^^ 


must  fulfill  our  three  conditions  (p.  40.)  .  In  fact  (Thiinen:  op.  cit.,  p.  121,  §14a)  , 
with  K  compared  to  D  the  physical  yield  of  rye  is  greater  everywhere  (1,710  >  1,000) , 
the  profit  per  hectare  greater  within  (for  instance  in  the  market  where  the  grower's 
price  is  1|  taler:  1,818  >  1,119)  ;  the  profit  per  bushel,  on  the  contrary,  is  smaller  even 
in  the  market  (1,818/1,710  <  1,119/1,000) .  Since  according  to  Thunen  {ibid.,  p.  36) 
the  yield  of  rye  would  be  proportional  to  the  total  yield  (which  we  rather  doubt) , 
this  example  would  generally  hold  also  for  a  comparison  of  both  production  systems 
as  a  whole. 

Historical  significance:  Thunen  proved,  in  opposition  to  Thaer,  that  adoption  of 
the  English  rotation  of  crops  is  advantageous  only  up  to  a  certain  distance  from  the 
market;  just  as  List  showed,  in  opposition  to  the  classical  writers,  that  free  trade  is 
profitable  onjy  from  a  certain  stage  of  development  onward.  In  other  words,  as  List 
proved  the  temporally  limited  validity  of  the  English  theories  of  the  time,  so  Thunen 
proved  their  spatial  limitation. 

26.  Exceptions  are  explained  by  the  fact  that  besides  location,  which  has  been  the 
sole  basis  of  our  theoretical  deductions,  other  factors  play  a  part  in  reality:  duties 
and  subsidies,  natural  fertility    (English  sheep  breeding  on  poor  soil) ,  freight  rates 

(coastal  regions  like  England  enjoy  cheap  sea  freights) ,  the  necessities  of  joint  pro- 
duction, extra-economically  conditioned  curbs  on  adaptation  to  new  situations,  and 
so  on. 

27.  See  G.  Pavlovsky,  "  Zur  Frage  der  raumlichen  Ordnung  der  Landwirtschaft," 
Internationale  Landwirtschaftliche  Rundschau,  I,  33    (1942)  ,  345  fF. 

28.  H.  Backe,  Utn  die  Nahrungsfreiheit  Europas    (Leipzig,  1942),  pp.  35-61. 


52 


Part  One.     Location 


§2.     Inversion  of  Thunen  Rings 
a.    Technique  of  Presentation 

We  shall  now  examine  the  formation  of  rings  according  to 
Thiinen's  theory  by  means  of  an  example  that  can  be  subsumed 
under  case  6  of  Table  2.  Twice  the  weight  of  potatoes  (I)  as  of 
corn  (II)  is  harvested  from  one  acre  with  the  same  outlay.  In 
order  for  rings  to  be  established,  the  further  conditions  (see  p.  92) 
nil  <  ^2  and  Ei/E2  >  mo/m^  must  be  met.  Since  Ei  =  2E2,  the  con- 
ditions can  be  rewritten  mi  <  ruz  <  2mi;  or,  since  a^  ==  2fli  also 
pi—ai<p2  —  2^1  <  2  (pi  —  tti) .  This  is  true  when  fli  <  po/2  and 
p2  —  ai>  pi>  P2/2.  We  start  out  from  a  price  limit  pi  =  6  and 
p2  =  12  per  hundredweight.  This  is  the  lower  limit  for  potatoes, 
for  if  the  price  sank  below  half  that  for  corn  no  more  potatoes 
would  be  raised.  At  these  prices  there  should  be  a  demand  for 
exactly  twice  as  many  hundredweight  of  potatoes  as  of  corn,  so 
that  the  area  devoted  to  both  will  be  the  same. 

In  order  to  simplify  Figures  7b  and  7d,  the  demand  curves  have 
the  same  slope,  which  involves  a  greater  elasticity  of  the  demand 
for  potatoes.  The  example  is  further  clarified  if  the  market  is 
regarded  as  a  line  rather  than  a  point  (like  a  river  valley  with  many 
towns) .  Then  the  rings  become  zones,  and  the  demand  is  propor- 
tional to  their  breadth.  We  also  assume  here— and  this  will  turn 
out  to  be  significant— that  the  commodity  with  the  higher  yield  per 
hectare  (potatoes)  will  be  cultivated  in  the  zone  nearest  the  market. 
This  will  be  true,  as  we  have  seen,  if  rings  are  formed  at  all.  Again, 
the  production  of  each  commodity  considered  alone  is  supposed  to 
be  in  equilibrium;  that  is  to  say,  neither  potatoes  nor  corn  yields 
a  rent  at  their  respective  margins  of  cultivation. 

As  for  the  technique  of  presentation,  it  should  be  noted  that 
the  scale  employed  for  the  quantity  of  corn  is  twice  that  for  the 
quantity  of  potatoes,  and  that  it  is  to  be  reckoned  from  the  actual 
boundary  between  I  and  II,  whereas  the  town  line  is  always  the 
zero  point  for  the  quantity  of  potatoes.  Thus,  in  contradistinction 
to  the  supply  curve,  the  demand  curve  N2  must  undergo  a  parallel 
shift  by  the  same  amount  and  in  the  same  direction  with  every 
shift  of  the  zero  point.  In  this  way  the  supply  curve  K  (production 
cost  plus  freight)  and  the  aerial  view  of  the  agricultural  area  can 
be  directly  compared.  The  production  costs  plus  freight  for  every 
point  in  the  area  can  be  read  off  from  a  point  directly  above  or 
below  it  on  the  corresponding  supply  curve. 


Agricultural  Location 


53 


A'  A 


s 

i 

Potatoes 

a 

a 

Corn 

- 

M 


0' 

1 
SO 

1  1 

[100 

N/ 

"^\ 

■^  Xvw 

b) 


M 

I  N^/    I  V; 

n 

}    XTr\ 

K, 

10 

r-A. >^--> 

Y" 

i 

r       /?;    rs^ 

Tn 

s 

7 

^^''^ — ^^K 

1 

6 

^^1  1 

\ 

5 

^^/    '  ' 

\ 

V 

-     ^,y^    1           1      I 

J 

--„y^           1            1      1 

1 

7 

■Centners  of  potatoes  (l)](7    | 

r 

0'             Wp\ 

'^^op 

Fig.  7.    Thiinen  case 


Fig.  8.  Inversion  of  the 
Thiinen  rings 


r  I  Part  One.     Localio)i 

54 

It  is  now  immediately  clear  that  no  equilibrium  exists.  At  the 
boundary  line  AB  in  Figure  1c  (which  gives  a  bird's-eye  view)  the 
rent  on  potatoes  is  0,  on  corn  R2S2,  per  hundredweight.  The  cultiva- 
tion of  corn  is  therefore  extended  at  the  expense  of  potatoes,  and  pz 
falls  to  po';  on  the  other  hand,  pi  rises  and  all  the  conditions  for  ring 
formation  are  now  fulfilled  (fli  =  2;  pi  =1.5;  p2  =  11.5;  substitu- 
tion in  tti  <  po/2  gives  2  <  3.75;  substitution  in  p2  —  ai>  pi>  p^/l 
gives  9.5  >  7.5  >  5.75) .  The  rent  changes  with  prices,  falling  for 
II  and  rising  for  I.  When  the  profit  on  a  hundredweight  of  potatoes 
is  equal  to  half  that  on  the  same  amount  of  corn  (i?iSi  =  RoSz/t) 
final  equilibrium  will  have  been  reached.  The  cultivation  of 
potatoes  is  then  diminished  by  the  area  A'B'BA,  total  cultivation 
by  the  smaller  area  C'D'DC.  So  far  everything  agrees  with  Thiinen's 
theory,  and  an  already  familiar  case  has  been  so  extensively  dis- 
cussed only  to  demonstrate  the  technique  of  presentation. 

jg.    Inversion  of  Rings 

We  shall  now  change  one  single  assumption.  We  shall  suppose 
that  potatoes  are  being  imported  from  America  and  that  the  fields 
lying  near  the  town  are  not  available  for  potato  raising,  their  use 
being  determined  by  long  tradition.  The  new  crop  is  therefore 
assigned  to  more  distant  fields,  where  an  unsuccessful  experiment 
will  not  cause  any  serious  loss  of  profit.  If  we  start  once  more 
from  the  same  situation:  equilibrium  for  each  individual  crop 
without  regard  to  alternative  possibilities,  potatoes  are  now  superior 
at  the  boundary  line  AB  (Fig.  8c) ,  where  corn  and  potatoes  meet. 
Their  cultivation  will  therefore  be  extended  at  the  expense  of  corn 
by  the  area  a  until  the  rent  of  corn  per  hundredweight  at  the 
boundary  line  A^B'  is  again  twice  that  of  potatoes;  the  return  per 
hectare  will  consequently  be  the  same  for  both  crops.  When  this 
point  has  been  reached,  equilibrium  apepars  at  first  to  prevail, 
although  the  Thiinen  rings  have  been  inverted! 

This  is  a  curious  situation.  Figure  8a  shows  ^^  that  a  shift  of 
the  boundary  toward  the  left  would  make  the  cultivation  of  corn 
at  the  new  boundary  more  advantageous,  and  that  a  shift  toward 
the  right  would  favor  the  cultivation  of  potatoes.  To  this  extent 
the  boundary  A'B'  in  Figue  8c  is  actually  the  only  possible  equi- 
librium position— so   far  as   equilibrium   really  is  decided  at   the 

29.  Figures  7a  and  8a  show  the  rent  per  hectare  at  the  boundary  as  a  function  of 
the  position  of  the  boundary. 


Agricultural  Location 


55 


boundary.  But  according  to  Figure  8e,  on  the  contrary,^"  the  boun- 
dary line  thus  found  marks  also  the  boundary  between  potatoes  and 
corn;  only  it  appears  (this  boundary  being  assumed  as  given)  that 
at  least  for  the  moment  it  will  be  more  advantageous  to  plant  the 
other  crop  at  every  point  away  from  the  boundary.  To  the  left  of 
the  dividing  line  the  cultivation  of  potatoes,  not  corn,  will  yield 
the  greater  rent  per  hectare;  the  reverse  is  true  to  the  right  of  the 
line. 

y.    The  Critical  Assumption 

The  contradiction  between  Figures  8a  and  8^    (summarized  in 
Fig.   9)    can   be  resolved. ^^    Suppose   it  has  already  been  decided 


z/'   ti 


Fig.  9.  Contradiction  between  figures  8a  and  8e.  la  and 
Ila  from  8a;  le  and  lie  from  8e 

Fig.  10.  Comparison  of  rent  per  hectare  in  Thiinen  case 
(continuous  line)   and  in  its  inversion   (broken  line) 

arbitrarily,  through  historical  accident  or  through  tradition,  that 
corn  will  be  raised  to  the  left;  the  planting  of  the  individual  farmer 
is  thus  controlled  by  his  environment,  which  leaves  him  a  choice 
only  at  the  boundary  line.  Under  these  assumptions  Figure  8fl 
shows  where  the  location  of  the  boundary  between  corn  (left)  and 
potatoes    (right)    will  finally  be  established. 

But  if  the  economic  spirit  is  revolutionary  rather  than  tradi- 
tional; if  each  farmer  doubts  the  whole  basis  of  the  customary 
agricultural  methods;  if  he  raises  the  question  of  the  most  advan- 
tageous choice  of  crops;  he  necessarily  encounters  the  situation  in 
Figure  8e.  Yet  it  would  be  shortsighted  for  all  farmers  to  the  left 
of  A'B'  (Fig.  8c)  to  change  over  suddenly  from  corn  to  potatoes, 
and  all  those  to  the  right  of  it  from  potatoes  to  corn,  because  a 


30.  Figures  le  and  8e  show  the  rent  per  hectare  as  a  function  of  distance  from  a 
market,  when  the  position  of  the  boundary  is  given. 

31.  la  and  Ila  from  Figure  8a;  \e  and  lie  from  Figure  8e. 


56 


Part  One.     Location 


larger  rent  was  promised  for  the  moment.  Obviously  that  would 
mean  disequilibrium.  Now  the  solution  in  Figure  7  would  hold, 
the  boundary  would  have  to  shift  toward  the  right,  prices  would 
fall,  and,  most  important,  all  rents  would  decrease  below  the  amount 
that  had  induced  the  farmers  to  change.  Nor  would  the  new  situa- 
tion be  advantageous  to  all.  The  dotted  line  in  Figure  10  shows  the 
rent  that  enticed  farmers  to  change  crops  (from  Figure  Se)  ;  the 
continuous  line  shows  the  rent  that  turns  out  to  be  lasting  after 


!!  Centners 

Potatoes  ^  C.       K  ^      Corn 
Die-hards 

Fig.  11.  Potato  market  (supply  and  rent  of  innovators,  OE,  and  die- 
hards,  B'F) 

Fig.  12.  Corn  market  (supply  and  rent  of  innovators,  FJ,  and  die-hards, 
EB') 

Fig.  13.  Rent  per  hectare  during  transition.  Broken  line,  former  rent 
(from  Figure  8e)  .  Continuous  line,  rent  during  transition  (from 
Figures  1 1  and  12) .  Horizontal  hatching,  gain  in  rent  compared 
with  the  former  condition;  vertical  hatching,  loss 

completion  of  the  change  (from  Figure  7e) ;  and  the  broken  line 
shows  the  rent  that  prevailed  before  the  revolutionary  change  (from 
Figure  8e) .  All  farmers  between  E  and  7^— sociologically  speaking, 
the  whole  rural  middle  class  or,  more  accurately,  the  entire  region 
of  moderate  ground  rent— will  have  lost  rent  (hatched  area  in  Figure 
10) .  Only  a  few  of  the  richest  farmers  (between  0  and  E)  and  the 
rural  proletariat,  and  only  on  the  soil  at  and  beyond  the  boundary 
(between  F  and  H)  ^^  will  have  gained. 

Will  the  farmers  between  E  and  F,  interested  in  preserving  the 
traditional  order,  be  able  to  obstruct  the  revolutionary  method  of 
planting  by  ^obstinately  continuing  to  cultivate  the  original  crop, 
giving  up  a  merely  transitory  advantage  in  order  to  acquire  greater 
rent  in  the  end?   The  change  to  potatoes,  profitable  under  all  cir- 

32.  This  agrees  with  our  earlier  calculation,  that  the  commodity  with  the  smaller 
yield  per  hectare  is  more  profitably  raised  at  the  periphery  of  the  cultivated  area,  the 
other  near  the  market.  The  intermediate  area,  for  which,  as  it  now  appears,  an  inver- 
sion of  the  Thiinen  order  may  be  advantageous,  was  not  considered  in  that  discussion. 


Agricultural  Location  57 

cumstances  between  0  and  £,  and  to  corn  between  F  and  H,  so 
lowers  the  price  of  both  that  the  rents  of  the  obstinate  ones  fall. 
Thanks  to  their  better  location,  the  rent  of  the  innovators  is  larger 
than  before,  in  spite  of  the  lower  price.  As  even  this  intermediate 
condition  is  more  profitable  to  them  than  the  old,  and  less  profitable 
to  the  obstinate  than  the  new  ^^  (see  Figs.  11  to  13) ,  it  must  prevail 
in  the  end.^* 

Thus  we  arrive  at  the  conclusion  that  in  a  dynamic  economy 
Thiinen  rings  must  be  formed^  whereas  in  a  traditional  economy 
their  reversal  may  held  equally  well.^^  The  sequence  of  the  rings 
cannot  be  proved  in  the  traditional  case  as  a  necessary  order,  but 
only  assumed  as  a  possible  principle  of  organization. 

§3.     Adjoining  Fields  Instead  of   Rings 

Suppose  that  an  equally  large  proportion  of  farmers  everywhere 
change  over  to  the  new  crop,  whereas  the  rest  keep  to  the  tradi- 
tional one;  or,  which  amounts  to  the  same  thing,  that  each  farmer 
plants  an  equally  large  area  of  his  fields  with  potatoes.  This  can 
be  most  simply  represented  by  having  the  two  crops  planted  not 
in  successive  rings,  but  in  adjoining  sectors.  A  change  in  the  width 
of  the  sectors  causes  a  rotation  of  the  supply  curve  about  its  inter- 
section with  the  price  axis.  Since  the  enlargement  of  one  sector 
necessarily  occurs  at  the  expense  of  the  other,  the  supply  curves  must 
always  be  rotated  in  opposite  directions.  It  is  immediately  apparent 
that  this  arrangement  results  in  equilibrium  only  under  special 
conditions.  It  is  always  possible,  to  be  sure,  to  change  the  width 
of  the  fields  in  such  manner  that  the  rent  at  the  periphery  of 
cultivation,  or  near  the  market,^®  will  be  the  same  for  both  crops. 
But  the  rent  is  equal  everywhere— and  without  this  there  is  no 
equilibrium— in  only  two  cases: 

33.  The  new  rent  to  the  farmers  between  E  and  F  is  given  approximately  by  the 
lower  broken  line  in  Figure  13.  It  is  thus  greater  in  any  case  than  the  transitional 
rent  shown  by  the  continuous  line. 

34.  Corn  will  be  planted  in  both  cases  only  between  G  and  B'    (Fig.  10) . 

35.  Of  course  this  reversal  is  not  desirable.  It  causes  unnecessary  freight,  and  less 
land  is  cultivated.  A  possible  exception  is  the  case  where  a  commodity  of  greater 
yield  per  acre,  but  lower  price,  pays  considerably  less  freight  per  mile. 

36.  In  this  case  the  fields  are  not  only  of  different  width,  which  would  not  be  bad, 
but  also  of  different  length.  Only  when  the  crop  with  the  smaller  yield  per  acre  (com) 
is  cultivated  farther  out  can  its  rent  by  the  hundredweight  at  market  be  greater  than 
the  corresponding  rent  for  potatoes.  And  only  when  the  rent  per  hundredweight  on 
corn  is  greater  is  the  rent  per  acre,  because  of  the  smaller  yield  per  acre,  equal  to  that 
for  potatoes. 


58 


Part  One.     Location 


1.  With  equal  yield  per  hectare  in  terms  of  weight  (Fig.  14)  ,^^ 
a  subcase  to  No.  18  in  Table  2.  The  radial  arrangement  offers  a 
possible  solution  only  in  cases  10,  14,  and  18  of  Table  2,  because 
in  the  others,  where  E^  =  E2,  the  remaining  conditions  impose  a 
restriction  on  the  production  of  one  commodity.    Or: 

2.  When  the  freight  charges  are  inversely  proportional  to  the 
yield  per  hectare.  This  must  be  distinguished  from  the  picture  we 
get  when  lines  of  communication  leading  out  of  a  city  pull  the 


•soil  (2) 


Fig.  14.  Illustration  of  case 
18  of  the  complete  system 


Fig.  15.    Mixed  cropping  and  rings 


37.  In  Figure  14  the  same  physical  yield  per  hectare  is  assumed  for  both  I  and  II. 
First,  let  each  of  the  two  equally  broad  fields  be  extended  in  a  direction  away  from 
the  market  (I  as  far  as  A,  II  as  far  as  B)  until  at  the  periphery  of  cultivation  the  rent 
everywhere  is  zero.  In  order  that  rent  at  the  market  and  the  length  of  the  fields 
shall  be  the  same  for  both  commodities,  field  II  is  broadened  at  the  expense  of  field  I 
(and  ATi  rotated  upward  thereby,  or  K^  correspondingly  downward)  until  rent  EF  is 
equal  to  rent  GH.  Both  fields  then  acquire  automatically  the  same  boundary,  A'B'. 
(However,  the  length  of  the  fields  can  now  no  longer  be  read  off  automatically  from 
the  supply  curves  K^'  and  K2,  as  was  still  possible  with  Kt^  and  K^.  To  this  end  it  is 
necessary  to  return  to  the  original  demand  curves,  where  the  points  /,  on  K^',  and 
D,  on  K^,  give  the  field  lengths.) 


Agricultural  Location  59 

rings  outward  to  such  a  degree  that  for  a  distance  they  are  almost 
parallel  to  these  lines.  Here,  however,  unlike  the  case  of  our 
sectors,  we  still  deal  with  actually  rather  than  virtually  separated 
zones.  For  it  should  be  clear  beyond  any  doubt  that  our  sectors 
are  only  an  especially  convenient  way  of  representing  adjoining 
fields. 

§4.     Adjoining  Fields  and  Rings 

There  still  remains  a  situation  in  which  sectors  (in  a  schematic 
presentation)  or  actually  adjoining  fields  (in  reality)  partially 
replace  rings:  where  soil  is  of  uneven  quality.^^  Of  course  in  those 
cases  where  a  definite  kind  of  soil,  in  comparison  with  another,  is 
more  fertile  for  all  products  in  the  same  proportion,  nothing  is 
altered  compared  with  the  partition  of  soils  of  equal  quality.  Either 
the  more  fertile  as  well  as  the  poor  soil  will  be  divided  between 
the  two  crops  (adjoining  fields) ,  or  both  will  produce  the  same 
(rings) . 

Not  so  when  soils  are  unequally  suitable  for  different  crops. 
Here  we  limit  ourselves  to  one  example.  Suppose  that  everywhere 
one  third  of  the  soil  is  of  quality  1,  which  produces  twice  the 
amount  of  potatoes  as  of  corn.  The  remaining  two  thirds,  of 
quality  2,  uniformly  produces  equal  physical  yields  per  hectare  for 
both  crops,  which  are  the  same  as  the  yield  of  corn  from  quality  1. 
Under  these  assumptions  it  is:  (a)  impossible,  as  long  as  both  crops 
are  cultivated,  that  the  better  soil  should  produce  anything  but 
potatoes,  regardless  of  the  distance  from  the  market.  For,  as  a  little 
study  of  Figure  15  will  show,  the  rent  from  potatoes  grown  on  the 
better  soil  equals  the  rent  that  corn  would  yield  on  it  (transpor- 
tation costs  of  the  physical  yield  of  corn  up  to  the  limit  for  cul- 
tivation of  corn,  C'E')  plus  the  rent  for  half  the  physical  yield  of 
potatoes,  calculated  as  freight  up  to  the  limit  for  potato  cultivation, 

(b)  It  is  impossible,  furthermore,  that  the  depth  of  cultivation 
on  the  better  and  the  poorer  soil  should  differ,  so  that  to  the  right, 
say,  of  AB  nothing  more  will  be  raised  on  the  better  soil.  For  since 
the  better  soil  is  always  as  suitable  for  corn  as  the  poorer  one, 
ABDC  will  inevitably  be  planted  with  corn.  This  lowers  the  supply 
curve  from  ML  to  MU.  But  since  potatoes  no  longer  yield  a  rent 
on  the  line  AB,  though  corn  does,  corn  growing  pushes  forward  on 

38.  Any  local  variation  in  production  cost  for  other  reasons  will  have  effects  similar 
to  those  of  variations  in  soil  quality. 


6o 


Part  One.     Location 


the  better  soil  toward  the  left  until  at  the  new  limit,  A'B',  the  same 
rent  per  hectare  ensues  for  both  crops  because  of  the  reduced 
cultivation  of  potatoes.  Calculated  per  centner,  the  potato  rent  is 
only  half  that  for  corn,  because  the  yield  of  potatoes  per  hectare 
is  twice  as  large.  This  shift  raises  the  supply  of  corn  by  the  yield 
of  the  area  A'B'BA,  and  the  greater  supply  so  lowers  the  price  that 
the  outermost  limit  of  cultivation  is  moved  backward  from  CE  to 
C'E\  As  a  final  result  we  have  adjoining  fields  of  the  crops  to  the 
depth  A'P",  which  wholly  corresponds  to  the  differing  soil  qualities; 
and  to  the  right  of  AT'  we  have  a  ring  of  production  of  the  same 
crop.^®'** 

b.     COMPREHENSIVE    SOLUTION 

We  must  now  separate  clearly  the  problems  of  location,  which 
so  far  have  interlaced,  and  consider  in  particular  another  important 
viewpoint:  joint  production  in  agriculture. 

§1.     The  Location  for  Agricultural  Production 

This  problem,  too,  divides  into  questions  respecting  the  location 
of  the  farm  and  the  location  of  the  products. 

The  problem  seen  from  the  standpoint  of  an  individual  farm 
is  merely  stated  here  and  not  solved,  in  order  not  to  repeat  ^^  the 
reasoning  already  developed  in  discussing  the  choice  of  an  indus- 
trial location.  This  problem  is  to  find  an  area  for  production  in 
such  a  region  and  of  such  a  size,  and  so  to  place  the  farm  therein, 
that  the  profit  shall  be  as  large  as  possible. 

But  on  what  part  of  the  farm  shall  a  certain  crop— say,  rye— be 
planted?  In  the  absence  of  joint  production  it  will  be  planted 
where  it  yields  a  higher  rent  than  any  other  crop.  But  it  is  not  a 
question  of  the  rent  from  rye,  or  from  single  fields,  but  from  the 

39.  The  area  for  corn  is  hatched. 

40.  By  a  somewhat  different  train  of  thought  T.  Brinkmann,  too,  arrived  at  the 
conclusion  that  the  whole  scale  from  extensive  to  intensive  cultivation  is  possible 
near  a  town  (radial  differentiation)  ,  whereas  with  increasing  distance  the  choice  is 
progressively  restricted,  poor  soils  are  abandoned,  and  goods  ones  must  be  cultivated 
extensively  (concentric  differentiation) .  ("  Die  Oekonomik  des  landwirtschaftlichen 
Betriebs,"  Gruiidriss  der  Sozialokonomik,  1922,  7  Abt.,  p.  46.) 

41.  Only  to  this  extent:  Upon  exact  consideration  (in  contrast  to  p.  29,  note 
31)  the  question  is  no  longer  one  of  locating  the  farm  so  that  the  paths  to  fields  for 
definite  crops  shall  be  as  short  as  possible;  for  the  intensity  of  cultivation  of  the 
individual  fields  depends  upon  the  exact  site  of  the  farm  (see  the  earlier  objections 
to  the  point  of  minimum  transport  cost) . 


Agricultural  Location  6^ 

farm  as  a  whole.*^  Thus  a  farmer  cannot  decide  where  to  plant 
rye  without  deciding  at  the  same  time  how  he  is  to  use  his  farm 
as  a  whole.  There  is  room  for  rye  only  as  it  fits  into  the  general 
production  scheme  (Betriebssystem) ,  only  as  it  promises  the  highest 
profit  to  the  farm  in  the  long  run.  One  must  be  clear  as  to  the 
consequences:  In  many  fields  rye  might  yield  the  highest  rent  pro- 
vided the  remaining  fields  were  employed  in  a  definite  way  (most 
favorable  for  the  cultivation  of  rye  in  the  particular  field  under 
consideration) .  Only  in  a  few  fields  will  the  rent  from  rye  still  be 
highest  even  when  every  field  is  cultivated  according  to  the  over-all 
plan,  in  such  a  way  that  the  profit  from  the  farm  as  a  whole  is  a 
maximum.  But  rye  will  not  be  grown  everywhere  that  it  yields 
the  highest  rent;  and  not  everywhere  that  it  is  cultivated  will  it 
produce  the  greatest  rent  attainable  from  this  field.  Nor  is  it  a 
question  of  the  change  in  total  rent  attributable  to  this  field,  since 
such  an  imputation  is  impossible,  for  reasons  given  on  p.  62, 
note  46. 

Total  profits  alone  are  decisive;  there  are  no  additional  criteria 
for  individual  crops.  Even  the  production  system  {Betriebssystem) 
that  would  be  most  advantageous  for  the  farm  cannot  be  scientifi- 
cally unequivocal,  as  a  rule,*^  but  can  be  determined  only  after 
experimentation;  even  then  uncertainty  would  still  remain,  since 
innumerable  combinations  are  possible  and  the  choice  among  them 
depends  in  general  upon  irregular  local  relationships  between  supply 
and  demand.  Nevertheless,  science  can  still  be  of  service,  as  it  is 
in  the  case  of  the  industries. 

The  general  distribution  of  farms  seen  from  the  standpoint  of 
the  economy  as  a  whole  will  be  discussed  in  Chapter  8.  Joint 
production  makes  it  difficult  to  determine  where  the  whole  of  one 
crop  will  be  produced— a  main  theme  in  one-sided  solutions— as  to 
determine  the  plan  for  the  use  of  the  land  on  an  individual  farm. 
The  rye  belts  of  the  world,  for  example,  cannot  be  fixed  without 
determining  the  location  of  all  other  belts  at  the  same  time,  and 
thus  in  the  end  the  geographical  distribution  of  the  production 
systems  of  individual  farms.  In  a  rye  belt,  therefore,  not  rye  as 
such  yields  a  maximum  profit,  but  a  production  system  that  includes 
the  cultivation  of  rye.  Rye  will  be  grown  wherever  a  production 
system  favorable  to  it  is  more  advantageous  than  any  that  excludes 
the  cultivation  of  rye. 

42.  Industrial  undertakings  with  joint  production  correspondingly  add  the  returns 
from  their  various  departments  and  from  their  various  products. 

43.  Except  with  simplifications,  as  on  p.  50. 


62  Part  One.    Localioji 

§2.  The  Agricultural  Production  of  a  Location 

Suppose  soil  qualities  to  be  irregularly  distributed  and  the 
markets  with  their  ruling  prices  ^*  given.  Let  the  production  at  all 
but  one  location  be  given  as  well.  It  is  required  to  find  the  pro- 
duction of  this  location.  If  it  is  a  field,  the  cultivation  of  all  other 
fields  (including  those  of  the  farm  concerned)  must  be  given;  if  a 
farm,  the  cultivation  of  all  other  farms. 

The  cultivation  of  a  field  is  not  determined  by  what  will  yield 
the  greatest  profit  on  it,  but,  because  of  joint  agricultural  pro- 
duction, by  what  will  yield  the  most  profit  to  the  farm  as  a  whole. 
The  same  end  will  naturally  be  sought  when  plans  for  the  use  of 
its  fields  have  to  be  formulated  anew.  These  plans  themselves 
depend  upon  market  prices  of  location  and  supplies,  and  the  com- 
position and  scale  of  output;  upon  the  relative  position  of  the 
various  fields  to  the  farm,^^  and  of  the  farm  itself  to  the  sales  market 
and  to  markets  for  the  factors  of  production;  upon  the  suitability 
of  soil  and  climate,  and  not  least  upon  the  skill  of  the  farmer;  upon 
the  advantages  of  mass  production  to  the  individual  farm  and  to 
other  farms  (thus  also  upon  what  is  cultivated  by  other  farms  in 
the  neighborhood)  ;  and,  finally,  upon  the  disadvantages  of  one- 
sidedness  already  discussed. 

Location  theory  can  say  no  more  on  the  subject.*®  It  may,  of 
course,  investigate  the  way  in  which  individual  factors  act  by  them- 
selves, as  has  been  done  under  (a) .  Their  co-operation  in  simple 
cases  is  discussed  by  locational  casuistics.  But  a  systematic  theory 
is  impossible  *^  because  of  the  endless  conceivable  differences  in 
situations  and  the  complexity  of  most.  Here,  too,  science  can  only 
indicate  individual  possibilities  that  deserve  special  investigation. 

44.  That  this  is  true  in  practice  because  of  the  radically  different  market  forms 
facilitates  matters  considerably  in  comparison  with  the  problem  of  industrial  location. 

45.  Cultivation  would  be  arranged  about  the  farm  building  also  in  Thiinen  rings 
if  location  alone  mattered.  The  fact  that  land  near  a  village  is  more  expensive  indicates 
that  location  plays  a  role  even  though  in  miniature,  provided  soil  quality  is  the  same. 

46.  Even  a  more  precise  characterization  of  the  maximum  is  difficult.  It  would  not 
be  correct  to  assume,  for  example,  that  the  partial  derivatives  of  cost  and  receipt  must 
be  equal  for  every  product.  It  is  more  likely  that  for  a  particular  marginal  combination 
the  costs  will  be  covered  by  the  receipts,  even  when  this  is  no  longer  true  of  every 
single  product  in  the  combination.  This  appears  to  have  been  overlooked  by  H. 
Marquardt  in  his  otherwise  excellent  presentation  (Die  Ausrichtung  der  landwirt- 
schaftlichen  Produktion  an  den  Preiseji  [Jena,  1934].  p.  80) ,  and  even  by  Schneider 

(Schmollers  Jahrbuch,  [1936],  213  ff.)  . 

47.  The  Thiinen  procedure  allows  only  an  analysis  of  the  influence  of  location,  and 
at  most  a  consideration  of  the  additional  effects  of  a  few  other  factors.    Its  further 


Agricultural  Location  63 

Unlike  those  of  industry,  however,  mere  calculations  certainly  do 
not  suffice,  because  relationships  are  in  part  too  difficult  and,  so  far 
as  they  are  determined  by  nature,  still  concealed  from  us.  Only 
actual  trial  (which  the  great  number  and  the  small  size  of  the 
interested  farms  make  more  easily  possible)  can  help;  indeed,  since 
some  effects  show  only  after  a  long  time,  only  extensive  experience 
can  give  an  answer.*^ 

c.     AGRICULTURAL    AND    INDUSTRIAL    LOCATION 
THEORY:    A    COMPARISON 


§1.     Different  Competitive  Situations 

One  of  the  main  differences,  at  least  in  a  brief  comparison  where 
certain  industrial  situations  resembling  the  agricultural  can  be 
neglected,  is  the  fact  that  in  agriculture  the  number  of  production 
locations  is  larger,  in  industry  the  number  of  locations  for  consump- 
tion. Hence  in  agriculture  producers  group  themselves  around  a 
consumption  site;  in  industry,  sites  of  consumption  about  a  pro- 
ducer. The  sales  market  for  agricultural  commodities  is  punctiform, 
whereas  that  for  industrial  commodities  is  areal.  The  latter  is 
supplied  by  one  or  a  few  industrial,  the  former  by  many  agri- 
cultural, enterprises.  Thus  the  typical  competitive  situation  for 
industry  is  limited  competition;  for  agriculture,  free  competition. 
This  means  much  less,  however,  than  appears  at  first  sight.  What 
effect  has  it  on  the  size  of  an  enterprise,  for  example,  that  in  indus- 
try the  demand  curve  for  the  single  firm  generally  falls,  whereas  in 
agriculture  it  is  horizontal?  At  first  it  might  be  thought  that  the 
entrepreneur  has  an  influence  on  the  price;  but  his  competitors  can 
affect  the  size  of  his  enterprise  by  alienating  customers:  partly 
through  situation,  partly  through  difference  in  product,  and,  when 
location  and  product  are  identical,  partly  through  their  mere  pres- 
ence. The  individual  farmer  has  no  influence  on  price,  but  in  return 
the  size  of  his  entreprise  is  independent  of  his  neighbors.  The  size 
of  his  farm  depends  upon  how  much  land,  not  upon  what  market, 
he  controls.  Geometrically  this  means  that  industry  produces  to 
the  left,  agriculture  to  the  right,  of  the  point  of  minimum  average 


extension  is  not  to  be  thought  of.  One  need  only  bear  in  mind  how  irregularly  pro- 
duction costs  vary  from  village  to  village  and  even  from  field  to  field  in  order  to  see 
immediately  that  there  is  no  general  procedure  for  deciding  on  an  agricultural  location, 
just  as  there  is  none  for  industry;  and  for  the  same  reasons. 

48.  Marquardt  shows  why  the  more  cautious  and  apparently  reactionary  farmers 
often  fare  better. 


64 


Part  One.    Location 


cost   (Fig.  16)  /^  or  at  that  point  if  ground  rent  is  included  in  the 
costs.  ^° 

But  this  apparent  difference  loses  its  significance  when  land  is 
freely  bought  and  sold  according  to  economic  motives  (and  only 
this  case  is  comparable  to  the  industrial) .  Here,  too,  the  extent  of 
a  farm  is  limited  by  the  tendency  toward  a  maximization  of  the 
number  of  independent  enterprises,  which  in  this  case  is  especially 
desirable. ^^ 


Fig.  16.   Size  of  the  producing  unit  in  a)  industry, 
b)  agriculture 


49.  Neither  excludes  an  optimal  supply  for  the  consumer,  however,  since  the  higher 
production  costs  may  be  more  than  compensated  in  the  first  case  by  savings  in  freight 
(reu  action  of  the  market  area) ,  and  in  the  second  by  a  fall  in  price  (increased  supply) . 
To  this  extent  the  complaint  of  an  industry  that  it  suffers  from  excess  capacity  is  irrele- 
vant, for  such  excess  capacity  is  in  the  interest  of  the  consumer. 

50.  This  is  easy  to  understand.  In  Figure  16b  let  TB  be  the  horizontal  price  line, 
Ki  the  average  cost,  and  OB  the  marginal  cost  curve.  The  firm  will  obviously  expand 
at  first  beyond  O  to  B,  at  the  intersection  of  the  marginal  cost  curve  with  the  price 
line.  But  rent,  TUOB,  is  a  cost  factor,  appearing  either  as  actual  rent  paid  or  as 
interest  on  the  value  of  the  land.  Hence  by  its  nature  rent  is  not  a  differential  but 
a  price  (see  J.  A.  Schumpeter,  "  Das  Rentenprinzip  in  der  Verteilungslehre,"  Schmollers 
Jahrhuch,  XXXI  [1907]) .  The  customary  presentation,  which  makes  it  appear  as  a 
residual,  is  in  reality  only  a  calculation  of  the  highest  amount  that  a  farmer  can  offer 
for  the  land.  For  nonagricultural  uses  there  are  other  values,  and  still  others  for  the 
rest  of  the  land,  and  the  price  of  land  for  industry  as  well  as  agriculture  is  derived 
from  this  competition  of  uses.  Suppose  this  system  to  be  such  that  a  farmer  obtains 
the  area  in  question  because  he  offers  the  most  for  it;  then  his  cost  curve  must  be 
shifted  upward  by  the  rent,  whose  total  amount  is  fixed.  B  is  the  low  point  on  the 
new  curve,  for  no  other  amount  of  production  can  support  such  a  high  rent.  Cham- 
berlin  used  this  new  cost  curve,  K2,  to  whose  minimum  point  the  demand  curve  is 
tangent,  for  industry  from  the  very  first.  He  regarded  rent  as  a  cost  factor  that  is  given 
from  the  beginning.  Thus  we  find  tangency  of  cost  and  demand  curves  a  criterion  of 
equilibrium  in  both  branches  of  the  economy. 

51.  A  farm  aiming  at  the  minimum  size  necessary  to  its  existence  could  add  land 
as  long  as  there  were  still  larger  farms  (unless  their  size  depended  upon  the  special 
ability  of  their  managers)  ,  merely  because  it  produced  larger  rent  and  therefore  could 
offer  a  higher  rental  or  a  higher  price.  Hence  it  would  buy  from  neighboring  farms 
the  fields  that  were  less  favorably  situated  for  them  than  for  it. 


Agricultural  Location  65 

The  limitation  works  in  a  downward  direction  also:  Even  where 
division  of  the  farm  through  inheritance  is  customary,"  farms  will 
be  reduced  only  to  a  size  actually  necessary  to  support  a  family.^^ 
The  maximization  of  the  number  of  producers  in  both  industry 
and  agriculture  is  thus  achieved  in  the  same  manner  despite  all 
formal  differences:  On  the  one  hand,  suitable  location  of  their 
locational  centers  (plants,  farm  buildings  ^*) ,  on  the  other,  the 
close  approach  of  competitors,  restrict  the  area  (sales  markets,  farms) 

52.  The  effects  of  a  financial  and  a  real  division  through  inheritance  must  be  dis- 
tinguished. The  former  cannot  render  a  farm  incapable  of  existence  if  its  value  is 
correctly  computed.  One  capitalizes  what  a  farmer  earns  above  what  he  would  earn 
in  an  occupation  without  capital— as  a  skilled  worker,  say.  A  farm  can  carry  that  much 
indebtedness.  Real  division  among  the  heirs  works  no  harm  either,  if  the  share  of  the 
retiring  heirs  remains  in  the  tenure  of  the  farm  or  (in  so  far  as  the  original  farm 
produced  more  than  enough  to  maintain  a  family)  is  used  to  improve  or  round  out 
other  farms.  The  evils  of  parceling  out  fields  (which  after  all  could  have  favored  a 
co-operative  spirit)  are  therefore  not  necessarily  associated  with  real  division.  Trouble 
will  arise,  however,  if  land  regularly  becomes  part  of  the  dowry  of  a  daughter  who 
marries  onto  another  farm.  In  considering  free  divisibility,  finally,  it  is  to  be  remem- 
bered that  with  improvements  in  agriculture  and  an  increased  demand,  especially 
during  the  past  century,  with  its  great  increase  in  population,  smaller  and  smaller 
farms  have  become  capable  of  existence.  Real  division  around  growing  towns  creates 
a  wholesome  transition  from  small  farmers  able  to  make  a  living,  through  commuters 
tied  to  the  soil,  to  free  industrial  workers. 

53.  This  is  not  extra-economically  determined,  as  it  were;  it  is  not  an  independent 
variable  at  all,  but  means  merely  just  enough  land  to  afford  a  farmer's  family,  with 
or  without  outside  help,  the  current  agricultural  equilibrium  income.  If  this  increases, 
the  optimum  size  of  the  farm  increases  as  well.  On  the  other  hand,  the  reverse  is  not 
necessarily  true:  When  the  most  profitable  size  of  a  farm  increases  in  the  course  of 
technical  development  (hitherto  it  has  decreased  for  many  crops;  see  H.  Priebe,  "  Zur 
Frage  der  Gestaltung  und  Grosse  des  zukiinftigen  bauerlichen  Familientriebes  in 
Deutschland,"  Berichte  uber  Landwirtschaft,  n.  s.,  XXVII  [1942],  523;  A.  Miinzinger, 
Bduerliche  Maschinengenossenschaft  Hdusern  [Berlin,  1934]) ,  the  rural  income  need 
not  increase.  The  competition  of  independent  farmers  would  cause  it  rather  to  fall, 
and  so  tend  again  to  reduce  somewhat  the  size  of  farms.  The  size  that  will  maintain 
a  family  at  any  given  time  is  set,  therefore,  in  addition  to  the  income  that  it  is 
supposed  to  yield,  by  the  other  factors  besides  area  on  which  this  income  depends: 
price  relations,  nature,  technique,  type  of  settlement,  division  of  fields,  law  of  inheri- 
tance, and  so  on.  Farms  of  a  few  hectares,  or  even  of  less  than  one,  that  are  near  a 
market  or  situated  in  a  fertile  area  can  make  an  adequate  profit  from  the  most 
promising  commodities  (fruit,  vegetables,  medicinal  plants,  flowers,  wine,  tobacco, 
poultry.  See  Priebe,  loc.  cit.) .  The  farm  with  a  small  income,  not  the  small  farm, 
should  vanish!  As  the  pay  of  rural  labor  at  equilibrium  should  be  adequate  for 
existence,  and  interest  on  the  value  of  the  farm  is  additional,  an  unencumbered  farm 
could  be  even  smaller  and  still  maintain  a  family. 

54.  Here  the  choice  of  a  location  must  be  considered  not  only  in  respect  to  the 
area  of  production  (the  farm's  own  fields  and  meadows) ,  but  also  in  respect  to  the 
situation  of  the  sales  market. 


56  Part  One.     Location 

to  the  minimum  necessary  for  existence  (that  is,  to  the  equilibrium 
size,  which  cannot  be  reduced  without  decreasing  the  number  of 
producers) . 

To  return  to  the  geometrical  picture  once  more:  As  intruding 
competitors  in  industry  restrict  the  sales  area  to  a  point  where  the 
demand  curve  shifts  toward  the  left  until  it  is  tangent  to  the  cost 
curve,  so  in  agriculture  they  restrict  areas  of  production  until  the 
cost  curve,  displaced  upward  and  to  the  left  by  addition  of  the 
ground  rent,  is  just  tangent  to  the  horizontal  demand  curve.  This  is 
the  counterpart  of  the  process  described  by  Chamberlin  and  Robin- 
son.^^  The  only  difference  is  that  in  industry,  depending  on  the 
competitive  situation,  the  cost  curve  is  given  and  the  demand  curve 
variable,  whereas  in  agriculture  price  is  fixed  and  costs  are  variable. 
In  either  case,  however,  the  variable  curve  is  shifted  for  the  same 
reason  and  with  the  same  result,  until  it  is  tangent  to  the  fixed 
curve.  In  short,  we  find  in  both  industry  and  agriculture  the  two 
important  forces  that  oppose  one  another  and  determine  location: 
a  tendency  to  maximization  of  the  number  of  producers  and  maxi- 
mization of  rent.^®  The  latter  is  well  known.  It  remains  to  sketch 
briefly  the  former. 

§2.     The  Common  Tendency  to  Maximization  of  the 
Number  of  Independent  Economic  Units 

The  longing  for  an  independent  and  established  life  in  harmony 
with  his  nature  is  deeply  rooted  in  man.  The  hope  for  an  indepen- 
dent existence,  more  than  any  alleged  material  advantage,  has  won 
over  the  nineteenth  century  to  the  idea  of  economic  freedom.  This 
goal  encouraged  inventors,  lured  the  pioneer  into  the  wild  West, 

55.  We  can  only  touch  upon  certain  complications.  When  farms  grow  smaller  the 
rents  of  the  owners  increase  and  the  income  of  the  actual  operator  decreases.  The 
former,  because  the  fields  in  general  now  lie  nearer  the  farmhouse  and  are  for  this 
reason  more  intensively  cultivated,  and  probably  also  because  of  the  smaller  size  of 
the  farm.  The  latter,  because  the  rent  now  goes  entirely  to  the  owner,  and  because  a 
small  farmer  needs  fewer  unusual  qualities.  The  average  cost  of  the  farm  rises;  its 
production  falls  as  a  whole,  but  increases  per  unit  of  area  until  the  point  is  reached 
where  any  further  diminution  in  the  size  advances  the  costs  per  hectare  more  than 
the  proceeds;  i.  e.,  until  the  land  rent  ceases  to  rise.  Then  the  agricultural  equilibrium 
income  is  reached,  for  the  rent  could  still  increase  if  this  were  too  high,  and  would 
have  to  fall  if  it  were  too  low. 

56.  Even  when  a  few  other  differences  between  agriculture  and  industry  are 
examined  (as  in  the  first  edition,  page  55)  ,  they  turn  out  to  be  of  little  weight,  so 
that  in  both  cases  the  problem  of  location  is  in  all  essentials  the  same,  in  spite  of  the 
different  competitive  situation  and  a  few  differences  in  degree. 


Agricultural  Locatiu7i  67 

drew  those  eager  for  great  undertakings  into  the  whirlpool  of 
competition,  and  made  unrestricted  divisibility  of  the  land  appear 
rational  to  able  farmer's  sons.^^  It  is  hard  to  say  whether  or  not 
these  expectations  were  fulfilled,  nor  did  the  reaction,^^  the  flight 
to  economic  security  at  the  price  of  independence,  fail  to  appear. 
The  wide  swing  of  the  pendulum  between  security  and  freedom 
can  be  traced  far  back  in  the  history  of  economics. '^^  Again  and 
again  we  find  periods  in  which  the  successful  strugglers  limited  the 
next  generation's  hope  for  independence  by  forcing  them  to  join  a 
guild,  or  obtain  licenses,  or  by  tying  them  to  the  land.  And  there 
were  times  when  they  prevented  entirely  the  success  of  these  aspira- 
tions through  closed  guilds  and  privileged  monopiolies  or  by  severely 
restricting  the  transferability  of  farms  or  prohibiting  new  invest- 
ments. This  was  followed  by  a  thinning  of  their  own  ranks  through 
competition  or  the  elimination  of  the  little  man  by  the  government. 
And  finally,  when  self-confidence  had  broken  down  because  of  per- 
sonal failure  or  force  majeure,  a  flight  to  the  protection  of  the  more 
powerful  followed,  such  as  the  transfer  of  free  farms  to  great  landed 
proprietors  in  the  early  Middle  Ages,  migration  of  artisans  to  the 
factories,  flight  to  a  cartel,  to  the  right  to  a  pension,  and  increasingly 
since  the  1870's,  to  government  security.  After  such  periods,  when 
the  barriers  between  economic  lords  and  serfs  are  open  only  in  the 
downward  direction,  confidence  returns  again;  social  tension  in- 
creases. Economically,  too,  men  wish  to  live  by  their  own  wills 
and  on  their  own  responsibility,  and  a  new  tendency  toward  the 
maximization  of  the  number  of  free  economic  units  sets  in. 


57.  Even  poor  districts  often  held  tenaciously  to  this  idea  to  permit  the  rise  of  the 
best  qualified  (H.  Rohm,  "  Das  bevolkerungspolitische  und  wirtschaftliche  Gesicht  des 
Dorfes  Gruibingen  1838-1938,"  Berichte  iiber  Landwirtschaft,  XXVI  [1940],  430) . 

58.  In  1882,  36  per  cent  of  the  German  working  population  were  independent. 
In  1933,  33  per  cent;  only  the  absolute  number  rose. 

59  At  the  margin  where  men  hesitated  between  dependent  and  independent  occu- 
pations, an  income  was  higher  in  this  or  that  case  according  to  whether  the  man  was 
ready  to  pay  the  price  of  security  or  of  freedom. 

60.  This  often  leads  to  violent  social  strife. 


Chapter  6.     Site  and  Reasons  for  Town  Settlement 


A  town  is  a  punctiform  agglomeration  of  nonagricultural  loca- 
tions. Now  the  question  arises,  why  there  should  be  in  any  particular 
place:  (1)  an  especially  large  enterprise,  (2)  a  collection  of  similar 
enterprises,  (3)  an  agglomeration  of  dissimilar  enterprises.  It  is 
well  to  distinguish  here  between  unrestricted  agglomerations  that 
could  form  anywhere,  and  those  restricted  to  a  particular  locality. 
Moreover,  from  the  first  we  shall  avoid  one  way  of  answering  these 
questions— mere  enumeration  of  the  good  features  of  a  location. 
These  are  not  always  essential  to  the  choice  of  any  particular  spot, 
and  when  they  are  necessary,  each  by  itself  is  inadequate.  A  seaport 
does  not  arise  on  every  natural  harbor.  It  must  be  proved,  rather, 
why  it  is  advantageous  for  some  entrepreneurs  to  avail  themselves 
of  these  favorable  features. 

a.     REASONS    FOR   TOWN    SETTLEMENT 

§1.     Unrestricted   Agglomeration    of  Locations 
(The   Natural   System) 

Even  though  the  earth  had  a  perfectly  uniform  surface  there 
would  still  be  towns. 

a.   Large  Individual  Enterprises 

The  advantages  of  mass  production  of  one  commodity  or  the 
joint  production  of  several  would  lead  at  some  locations  to  the  estab- 
lishment of  a  greater  assemblage  of  production:  a  factory.  This  may 
be  so  large,  indeed,  as  to  constitute  a  town  by  itself  (Siemensstadt, 
Stadt  des  KdF-Wagens) .  (Gary,  originally;  Radford,  Va.,  World 
War  II;  Oak  Ridge,  Tenn.,  and  Hanford,  Wash.,  atomic  energy; 
Longview,  Wash.,  lumber;  Anaconda,  Mont.,  copper  smelting.) 

j8.   Agglomeration  of  Similar  Enterprises 

1.    advantages   of   numbers  and  association 

In  some  places  a  number  of  similar  enterprises  will  establish 
themselves,  partly  because  this  increases  the  demand  for  each  one 

68 


Reasons  for  Town  Settlement  69 

individually  since  buyers  like  to  purchase  certain  differentiated 
goods  where  they  can  compare  different  varieties,  partly  for  the 
sake  of  those  advantages  which  reduce  the  cost  of  all  and  which 
are  summarized  as  external  economies  (large  labor  market,  more 
efficient  auxiliary  industries,  mutual  stimulation,  special  fittings, 
and  so  on)  .^ 

2.   ADVANTAGES  OF  SITE  AND  SOURCE  OF  SUPPLY 

Production  may  also  gravitate  to  one  place  because  it  is  tech- 
nically tied  to  an  important  source  of  the  raw  materials  and  inter- 
mediate products  that  it  uses;  or  because  it  is  technically  tied  to 
consumers,  as  is  the  case  with  craftsmen  or  merchants,  for  example. 
Or  it  may  simply  be  attracted  by  a  large  labor  market,  a  considerable 
local  demand,  contact  with  government  agencies,  traffic  junctions,  or 
the  proximity  of  other  towns.  Such  advantages,  which  are  limited 
to  a  few  places,  occur  also  with  natural  uniformity,  as  we  shall  see 
later  in  the  model  of  a  simple  system  of  economic  areas.  Locations 
like  these  are  especially  rare  and  at  the  same  time  especially  favored 
in  systems  of  equal  structure  (see  pp.  130  ff.) .  The  fewer  possible 
market  areas  we  assume,  the  larger  becomes  the  number  of  goods 
whose  markets  around  their  possible  locations  is  greater  than  is 
necessary  for  the  mere  survival  of  the  individual  firm. 

3.      INTERNAL    COMPETITION 

(aa)  Division  of  Local  Demand.  All  these  advantages  influence 
an  enterprise  established  at  a  favored  site,  partly  through  lower  costs 
and  partly  through  increased  demand.  Such  an  enterprise  can  hardly 
be  affected  from  outside,  i.  e.,  by  neighboring  competitors.  Its  pro- 
duction cost  may  be  so  low  that  another  enterprise  can  survive  only 
at  a  considerable  distance.  When  the  great  demand  comes  chiefly 
from  the  location  of  the  first  enterprise  itself,  it  is  impossible  for  a 
distant  competitor  to  attract  part  of  it.  In  short,  the  Chamberlin 
process  (see  pp.  109  ff.),  which  depends  on  the  tendency  toward  a 
maximization  of  the  number  of  independent  firms,  cannot  be  carried 
on  from  outside  against  the  favored  enterprise.  Instead,  competi- 
tion starts  from  within.    When  this  leads  to  division  of  a  town 

1.  See  the  excellent  study  of  the  town  of  Pirmasens  by  E.  Schuster  et  al.,  Mono- 
industrielle  Agglomeration.  Die  Schuhindustriestadt  Pirmasens  (Wiirzburg,  1940) .  In 
Pirmasens  only  shoe  factories  are  agglomerated  because,  among  other  reasons,  they 
completely  exhaust  the  supply  of  every  kind  of  labor  available.  That  this  is  unusual 
another  reason  for  association,  and  should  be  added  to  those  discussed  below  on 
pp.  75-76  and  88-89. 


70 


Part  One.     Location 


among  the  various  enterprises  assembled  there,  the  situation  is 
fundamentally  normal.  Measured  by  the  number  of  establishments 
(or  enterprises) ,  the  agglomeration  will  become  more  intense  the 
smaller  the  size  of  the  firms  in  an  industry  at  Chamberlin's  point. 

(bb)  Supplying  the  Same  Market.  But  what  would  happen  if 
not  the  local  demand  is  divided,  but  the  demand  from  the  market 
area  in  respect  to  which  the  individual  enterprises  enjoy  practically 
no  locational  advantages  over  one  another?  Let  N,  in  Figure  17,  be 
the  demand  curve  of  the  first  enterprise  to  establish  itself  and  K-^^ 
its  average  cost  curve.   As  an  almost  unrestricted  monopoly,  it  sets 


Amount  V 

Fig.  17.   Supply  of  the  same  market  by  several  entrepreneurs 

its  price  near  Cournot's  point.  But  a  second  and  a  third  competitor 
appear.  Is  N  still  valid  for  all,  or  will  it  be  broken  into  three  partial 
demand  curves?  In  other  words,  will  the  demand  curve  of  the  first 
firm  be  gradually  rotated  downward  and  toward  the  left,  as  in  the 
Chamberlin  process,  until  finally,  as  rii,  it  is  just  tangent  to  K^} 
Such  a  tendency  might  continue  in  a  few  firms  because  personal 
characteristics  of  the  entrepreneurs,  or  advertising,  etc.,  draw  atten- 
tion to  the  firm  and  are  important  in  the  particular  case.  But  the 
more  competitors  there  are,  the  flatter  each  partial  demand  curve 
becomes;  that  is,  the  more  sharply  demand  reacts  on  each  price 
change  of  a  single  firm.  We  are  aproaching  pure  competition  and 
shall  have  reached  it  when  the  partial  demand  curves  become  so 
flat  that,  in  the  long  run,  an  enterprise  offering  its  goods  at  a  little 


Reasons  for  Town  Settlement  7^ 

above  the  equilibrium  price  can  hardly  continue  to  sell,  whereas 
were  it  to  cut  the  market  price  a  little  it  would  sell  all  that  it 
could  possibly  produce. - 

The  partial  demand  curve,  rV ,  of  a  given  firm,  r,  coincides  at 
F  and  V  actually,  and  throughout  the  remainder  of  its  length  prac- 
tically, with  the  broken  line  FBCV,  and  where  it  deviates,  it  lies 
slightly  to  the  right  of  FB  and  at  first  somewhat  above  and  then 
somewhat  below  BC.  In  its  last  portion  it  is  virtually  identical 
with  the  aggregate  demand  curve.^ 

What  is  the  shape  of  the  supply  curve?  With  the  appearance 
of  new  competitors,  external  economies  may  at  first  lower  the  cost 
curve  of  the  first  enterprise  from  K^  to  K.  Now  workers  of  all 
degrees  of  efficiency  crowd  into  the  competing  enterprises.  Some  of 
these  firms  can  secure  expensive  sites  near  the  railroad  station, 
whereas  others  must  be  satisfied  with  cheaper  but  less  favorable 
sites.  Despite  these  differences  all  cost  curves  must  be  the  same,  if 
the  productivity  of  the  factors  of  production  varies  only  with  the 
degree  to  whicli  the  capacity  of  the  plant  is  utilized  and  otherwise 
remains  constant.  The  differences  in  the  cost  curves,  as  the  figure 
shows  (^1  need  not  be  the  lowest  one  by  any  means) ,  rest  solely 
upon  the  varying  ability  of  entrepreneurs  to  use  their  factors  of 
production  effectively.* 

2.  We  can  imagine  the  gradual  increase  in  the  anonymity  of  the  individual  firm 
by  supposing  that  with  a  sufficiently  large  number  of  small  enterprises  a  particular 
firm  buys  their  products  and  retails  them  in  the  vicinity. 

3.  It  would  be  meaningless  to  derive  the  aggregate  demand  curve  by  adding  these 
partial  demand  curves,  because  they  are  not  independent  of  one  another. 

4.  Theoretically  it  might  be  expected  that  each  entrepreneur  would  pay  every  factor 
of  production  according  to  its  marginal  product,  and  that  this  output  would  be  the 
same  whether  the  last  unit  of  the  factor  were  employed  by  the  marginal  entrepreneur 
or  by  a  superior  one.  What  more  the  latter  was  able  to  extract  from  it  would  have 
to  be  balanced  by  the  disadvantages  of  exceeding  the  optimum  size  of  the  firm.  Where 
the  marginal  worker  (as  seen  by  the  individual  firm)  could  be  distinguished  from  other 
workers,  all  would  have  to  be  paid  according  to  output,  unless  their  greater  output 
was  due  to  their  own  skill  rather  than  to  their  position  in  the  factory.  In  so  far  as 
the  former  is  true,  it  should  make  no  difference,  therefore,  whether  a  good  or  a  poor 
worker  was  employed,  since  each  would  be  paid  according  to  his  productivity.  In 
reality,  the  better  enterpreneurs  secure  the  better  workers  as  well  the  better  sites  and 
pay  them  higher  wages  than  they  could  get  from  the  marginal  entrepreneurs.  The 
reason  is  that  these  workers  need  less  supervision  because  of  their  personal  charac- 
teristics, and  that  they  make  less  demand  per  unit  of  output  on  the  entrepreneur's 
time  (indirect  efficiency)  ,  so  that  through  them  he  can  achieve  greater  profits  within 
the  limits  of  his  own  ability.  In  its  details  the  determination  of  wages  is  exceedingly 
complicated,  of  course,  if  labor  is  subdivided  into  groups,  and  only  the  qualitative 
and  quantitative  peculiarities  of  the  efficiency  of  the  individual  are  stressed. 


72 


Part  One.     Location 


The  total  cost  curve  is  now  constructed  from  the  individual  cost 
curves.  Let  the  market  price  rise  slowly.  Each  firm  begins  to  operate 
when  the  price  line  touches  its  point  of  minimum  average  cost. 
If  the  price  goes  higher,  it  follows  its  marginal  cost  curve,  k',  up  to 
its  intersection  with  the  price  line.  The  discontinuous  horizontal 
jumps  of  the  aggregate  supply  curve  show  that  a  new  factory  has 
become  able  to  compete.  The  smaller  these  jumps,  that  is,  the 
smaller  the  optimum  size  of  a  firm  in  the  particular  industry,  the 
greater  the  agglomeration  of  firms  will  be.  The  portions  of  curves 
between  two  jumps  are  obtained  by  adding  all  marginal  cost  curves, 
in  so  far  as  they  lie  to  the  right  of  the  minimum  average  cost  and 
within  the  relevant  price  intervals.  From  this  it  follows  that  every 
producer,  after  having  entered  the  total  supply  curve,  is  represented 
in  every  portion  of  it.  If  all  entrepreneurs  were  equally  efficient 
the  supply  curve  would  necessarily  be  horizontal  (As) .  This  would 
exclude  special  profit  and  would  correspond  to  tangency  in  the 
Chamberlin  process.  The  agglomeration  of  factories  would  then  be 
still  greater;  first,  because  the  size  of  each  would  be  less;  second, 
because  at  the  lower  price  the  demand  from  the  original  market 
area  would  be  greater;  and  third,  because  the  area  itself  would  be 
enlarged.  The  last  two  effects  have  been  taken  into  account  in  our 
demand  curve.^ 

4.     hotelling's    case 5" 

Here  would  belong  also  that  tendency  toward  agglomeration 
which  is  based  on  freight  cost  and  which  Hotelling^  has  tried  to 
demonstrate.  He  assumed  two  competitors  along  a  finite  stretch 
(such  as  two  ice  cream  vendors  along  a  beach)  with  an  inelastic 
demand.  The  location  of  at  least  one  of  the  two  is  mobile,  and  the 
f,  o.  b.  prices,  which  are  uniform  for  all  customers,  are  changeable. 
In  setting  his  own  factory  price,  every  competitor  assumes  that  the 
price  of  his  rival  is  fixed.  Under  these  assumptions  Hotelling  shows 
that  the  location  which  is  most  favorable  from  the  standpoint  of 
the  individual  firm  does  not  coincide  with  the  economically  most 
desirable  location  of  minimum  freight  cost.  The  location  that  would 
minimize  freight  cost  would  be  at  a  distance  of  one  quarter  of  the 
total  length  of  the  stretch  from  each  end.  In  fact,  however,  each 
competitor  finds  it  advantageous  to  move  close  to  the  other. 

5.  On  the  proliferation  of  factories  in  Pirmasens  see  E.  Schuster  et  al.,  Monoindus- 
trielle  Agglomeration.   Die  Schuhindustriestadt  Primasens   (Wiirzburg,  1940) ,  p.  22. 

5a.  Section  4  has  been   translated  from   the  first   German  edition,  pp.    12-15,  for 
insertion  here  where  Losch  had  omitted  it  to  save  space. 

6.  H.  Hotelling,  "  Stability  in  Competition,"  Economic  Journal,  1929. 


Reasons  for  Town  Settlement  73 

The  objections  against  this  derivation '  are  that  it  is  valid  only 
under  very  unusual  circumstances.  The  first  group  of  objections 
concerns  unlikely  behavior  of  the  rivals.  First,  it  is  hardly  likely 
that  one  duopolist  will  assume  that  his  rival  will  not  react  to  his 
own  actions.  As  soon  as  this  assumption  is  dropped  we  find,  as 
Palander  has  shown,  "  a  pronounced  tendency  toward  deglomera- 
tion."  ^  If,  for  example,  both  duopolists  act  alike,  the  optimal 
location  for  each  is  one  sixth  of  the  length  of  the  whole  stretch 
from  each  end.  Here  is  a  second  improbability:  Why  should  the 
two  duopolists  act  differently  if  all  circumstances  confronting  them 
are  identical  for  both?  It  is  true  that  the  more  symmetrically  the 
competitors  are  located  along  our  stretch,  the  greater  will  be  the 
profit  for  both  of  them  together.  But  the  distribution  of  this  profit 
would  be  equally  asymmetrical,  and  why  should  the  competitor  who 
finds  himself  on  the  short  end  be  content  with  such  a  situation? 

Symmetrical  possibilities  are  rather  more  probable.  Either  we 
permit  the  first  competitor  to  locate  himself  in  the  center  from  the 
very  beginning,  in  which  case  the  best  thing  his  rival  can  do  is  to 
imitate  him  and  do  likewise;  or  else  the  first  places  himself  asym- 
metrically on  the  stretch.  Then  the  other  will  settle  near  him  but 
on  the  longer  end  of  the  stretch.  In  the  next  round,  however,  the 
first  will  jump  over  him,  and  the  two  will  dance  around  one  another 
until  they  have  reached  the  center.  Or  else  both  will  start  at  the 
same  time  and  place  themselves  simultaneously,  either  in  the  center 
or  at  any  symmetrically  located  points  on  the  stretch.  In  the  latter 
case— and  the  central  location  is  after  all  only  the  limiting  case— the 
profit  (of  each  one  separately  and  of  both  together)  will  be  every- 
where the  same,  however  unlikely  this  may  sound.  This  follows 
immediately  from  the  profit  formula.  Consistently  pursued.  Hotel- 
ling's  case  leads,  under  his  own  assumptions,  to  the  result  that  it  is 
completely  irrelevant  for  both  enterprises  where  they  will  locate 
as  long  as  they  are  located  symmetrically.  (Hotelling  himself  con- 
siders symmetry  merely  "  improbable,"  without  excluding  it  by  his 
assumptions.) 

The  result  is  valid  only  if  both  rivals  assume  in  their  price  policy 
that  they  have  to  share  the  market.  But  this  assumes  a  great  lack 
of  foresight  and  this  is  the  third  improbability  of  their  behavior. 
Palander  ^  shows  that  the  interaction  of  two  possible  behavior  pat- 

7.  The  mathematics  will  be  found  in  Hotelling,  op.  cit.,  and  in  even  more  general 
form  in  Tord  Palander,  Beitrdge  zur  Standortstheorie   (Uppsala,  1935) ,  pp.  232-235. 

8.  Palander,  op.  cit.,  p.  394. 

9.  Op.  cit.,  pp.  237  ff. 


74 


Part  One.    Location 


terns  will  lead  to  continuous  price  fluctuations,  and  this  is  true  even 
when  the  firms  are  still  fairly  distant  from  each  other,  but  is  certainly 
true  when  their  distance  from  each  other  equals  half  the  length  of 
the  stretch.  Hotelling's  formulas  indicate  that  the  price  and  the 
profit  of  that  rival  who  moves  nearer  to  the  other  will  rise.  Instead 
of  increasing  his  price  also  and  thus  sharing  the  intermediate  stretch 
with  the  aggressor,  the  duopolist  attacked  will  find  it  more  profitable 
after  a  certain  distance  to  lower  his  price  and  thus  either  crowd  the 
aggressor  out  of  the  market  entirely  or  force  him  to  lower  his  price. 
Hotelling  does  not  consider  this  possible  behavior.  Such  a  price 
reduction  means  that  the  rivals  will  move  farthest  apart,  until  the 
critical  distance  has  been  reached,  when  an  increase  in  price  will 
again  appear  to  be  more  favorable.  The  cause  of  this  incessant 
fluctuation  lies  in  the  assumption  that  the  rival  will  keep  his  price 
unchanged.  This  assumption  drives  both  rivals  beyond  the  stretch 
within  which  an  equilibrium  would  exist,  which  is  bounded  by 
the  end  points  and  the  quarter  points  of  the  stretch. 

The  second  group  of  objections  is  directed  against  unlikely  cir- 
cumstances. First,  Hotelling  assumes  a  completely  inelastic  demand, 
which  is  a  rare  case.  Hotelling  told  me  he  would  agree  that  with  an 
elastic  demand  there  would  be  a  tendency  for  the  rivals  to  move 
into  the  neighborhood  of  the  quarter  points.  I  would  go  even 
farther:  In  the  case  of  an  elastic  demand  an  enterprise  will  locate 
exactly  at  the  quarter  point  if  it  selects  an  equilibrium  point  at  all, 
since  every  other  point  lies  asymmetrically  in  the  market  and  thus 
limits  demands  and  profit  possibilities. 

The  situation  changes,  secondly,  if  more  than  two  producers  are 
assumed.  Hotelling  might  salvage  his  argument  for  several  com- 
petitors by  abandoning  the  line  for  an  area.  On  the  other  hand,  for 
the  line— and  this  is  true  also  for  a  larger  area— Chamberlin  shows 
that  more  than  two  producers  would  spread  out  even  under  Hotel- 
ling's  own  assumptions.^"  The  intermediate  producers  are  all  equally 
spaced  from  each  other.  If  one  of  them  moved  nearer  to  his  right- 
hand  neighbor,  for  example,  he  would  lose  as  much  area  to  his  left- 
hand  competitors  as  he  gains  from  the  one  on  his  right.  Nevertheless, 
Chamberlin  overlooks  the  fact  that  such  an  asymmetry  might  be 
profitable  for  him  if  it  were  an  equilibrium  position.  But  equi- 
librium exists  now  only  if  the  rivals  are  equidistant.  However,  even 
independent  of  any  considerations  of  equilibrium  Chamberlin  is 
correct:  It  is  impossible  that  more  than  two  entrepreneurs  approach 

10.  E.  H.  Chamberlin,  The  Theory  of  Monopolistic  Competition   (Cambridge,  Mass., 
1936) ,  pp.  194-196. 


Reasons  for  Town  Settlement  75 

each  other.  A  third  producer  who  was  located  between  them  would 
always  gain  by  jumping  over  either  his  rival  to  the  right  or  his  rival 
to  the  left.  Only  the  producers  at  the  ends  of  the  stretch  have  an 
area  one  and  a  half  times  as  great  as  that  of  the  others.  As  long  as 
they  remain  on  the  interior  third  point  of  the  end  portion  of  the 
stretch,  none  of  the  rivals  has  any  incentive  to  jump  over  them  and 
become  an  end  man.  To  this  extent  one  might  speak  of  a  tendency 
to  an  agglomeration  toward  the  middle. 

But  even  this  tendency  disappears  completely  if  we  drop  the 
third  restriction.  Suppose  we  have  an  endless  stretch— an  assumption 
quite  permissible  if  we  are  thinking  of  conditions  on  earth.  In  this 
case,  each  of  the  two  competitors  with  a  finite  maximum  delivery 
distance  would  gain  by  moving  apart  until  there  arose  between  them 
a  completely  unsupplied  area.  Even  more  appropriate  for  this  earth 
would  be  the  substitution  of  a  circle  on  a  sphere  for  our  stretch. 
If  one  of  the  competitors  remains  in  place  while  the  other  approaches 
him,  the  "  back  end  "  of  his  half  of  the  circle  will  become  larger 
and  larger.  But  unlike  the  case  where  the  rivals  are  situated  on  a 
plane  stretch,  the  "  back  end  "  of  his  rival's  part  of  the  circle  in- 
creases equally  at  the  same  time.  Since  according  to  the  formula, 
however,  profit  increases  with  the  difference  of  the  two  ends,  and 
since  this  difference  remains  zero  for  every  position,  it  follows  that 
on  a  circle,  the  situation  on  a  finite  stretch,  it  is  useless  for  one 
competitor  to  approach  the  other  even  if  one  is  immobile. 

Since  Hotelling's  "  tendency  to  agglomeration  "  has  created  some 
furore  and  has  led  to  considerable  and  fruitful  discussions  in  which 
not  all  participants  sided  against  Hotelling,  it  was  necessary  to  scru- 
tinize his  interesting  thesis  in  some  detail.  We  conclude  that  under 
assumptions  with  even  a  slight  degree  of  realism,  no  such  tendency 
to  agglomeration  conditioned  by  freight  cost  exists. 

y.    Agglomeration  of  Different  Enterprises 

4.      AGGLOMERATION    THROUGH     INTERRELATIONSHIP 

(aa)  Advantages  of  Numbers.  There  are  common  advantages 
to  producers  in  the  agglomeration  at  one  place  of  a  moderately  ^^ 
large  output,  no  matter  of  what  kind.    One  of  the  most  important 

n.  There  is  an  optimum  point  beyond  which  confinement  to  a  town  tends  to  raise 
costs.  The  growth  of  towns  is  slowed  on  the  one  hand  by  the  increasing  disadvantages 
and  cost  of  crowding,  which  manifest  themselves  particularly  as  traffic  slowdowns  and 
rising  land  prices,  and  on  the  other  by  the  increasing  disadvantages  and  cost  of  dis- 
tance from  places  of  work  and  from  sellers  of  agricultural  and  buyers  of  industrial 
products.    These  costs,  to  be  sure,  have  been  shifted  in  part  to  the  general  public; 


1^6  Pa'>'t  One.     Location 

is  the  advantage  of  having  a  railway  station,  not  to  mention  better 
streets  and  drainage,  cheaper  water  and  electricity,  and  a  larger 
labor  market. 

(bb)  Advantages  of  Association.^^  First,  under  any  given  market 
situation:  The  preference  of  consumers  for  combining  small  pur- 
chases or  comparing  various  qualities  of  differentiated  products  is 
hardly  less  important  for  the  formation  of  towns  than  for  the  exis- 
tence of  special  business  districts  within  a  town  and  of  department 
stores  in  these  districts.  The  mere  fact  of  their  proximity  not  only 
lowers  the  cost  of  production,  especially  general  costs,  but  at  the 
same  time  increases  the  share  of  the  demand. 

Second,  with  economic  fluctuations:  It  is  advantageous  for  a 
place  to  harbor  industries  whose  seasonal  or  cyclical  variations  do 
not  coincide.  Of  course  this  alleviates  not  these  fluctuations  them- 
selves, but  their  reinforcing  secondary  effects  on  enterprises  that  are 
directly  concerned,  such  as  local  handicrafts  and  business. 

Third,  with  structural  changes  in  the  economy:  Structural 
changes  in  the  economy  are  easier  to  cope  with  when  a  population 
has  varied  interests,  activities,  and  characteristics.  On  such  a  soil, 
as  List  emphasized,  ingenuity  and  adaptability  flourish  more  readily 
and,  in  addition,  the  well-balanced  culture  that  is  not  only  admir- 
able in  itself  but  fruitful  for  independent  and  adaptation  to  new 
situations. 

Fourth,  more  general  reasons:  The  ablest  members  of  all  pro- 
fessions and  trades  which  are  not  tied  down  to  particular  places, 
who  therefore  can  live  where  they  wish  and  are  in  general  the 
bearers  of  a  conscious  cultural  tradition,  tend  to  attract  one  another 
and  thus  increase  their  achievements  and  their  enjoyment  of  life. 

(cc)  Advantages  of  Proximity,  etc.  First,  for  "city  fillers":  W. 
Sombart  ^^  drew  an  admirable  distinction  between  "  city  founders  " 
and  mere  "  city  fillers  ";  i.  e.,  between  occupations  that  establish 
cities  and  those  that  exist  because  a  city  is  already  there."   By  ful- 


for  example,  in  the  case  of  expensive  railway  terminals  in  metropolitan  centers  and 
of  the  expensive  supply  installations  of  suburban  settlements,  but  also  through  the 
prevention  of  speculation  in  land.  In  order  to  cavise  large  cities  to  spread  out  it  would 
have  been  better,  while  there  was  still  no  municipal  planning,  to  tax  land  speculation 
severely  but  without  actually  preventing  it. 

12.  These,  too,  represent  common  external  economies. 

13.  Der  moderne  Kapitalismus,  I  5.  A    (1922)  ,  pp.  131  f. 

14.  This  is  a  special  case  of  the  general  difference  between  occupations  that  deter- 
mine, and  occupations  that  are  determined  by,  location.  In  a  rough  classification  the 
former    generally    include    agriculture,    mining,    and    some    manufactures;    the    latter 


Reasons  for  Town  Settlement  77 

filling  a  function  for  a  smaller  or  larger  surrounding  area  the  former 
create  claims  on  the  outside  world,  so  to  speak,  in  return  for  which 
its  commodities,  and  especially  agricultural  products,  are  brought 
into  town.  The  latter  work  for  the  former  or  are  otherwise  tied  to 
their  locations:  local  trades,  i.  e.,  trades  with  a  very  small  market 
radius;  ancillary  industries;  but  also  certain  finishing  trades  as  well  as 
complementary  enterprises  such  as  the  textile  industry,  which  gives 
work  to  the  wives  of  the  men  employed  in  heavy  industry.  None 
of  these  would  exist  in  the  absence  of  the  founding  occupations. 

Second,  for  "  city  founders  ":  In  one  case  "  city  fillers  "  rise  to 
the  rank  of  "  city  founders."  It  is  advantageous  in  every  economic 
region  to  have  the  market  networks  for  individual  goods  coincide 
at  one  point,  as  we  shall  see  later.  This  metropolis,  to  be  sure, 
fulfills  functions  for  the  whole  area,  but  its  functions  could  be  ful- 
filled also  if  the  market  networks  were  set  down  indiscriminately. 
Aside  from  the  reasons  previously  given  they  will  meet  in  one  place 
because  industries  largely  determined  by  consumption  mutually 
create  in  this  way  the  advantages  of  a  large  local  demand  for  each 
other.^^  These  advantages  consist  partly  in  the  feasibility  of  more 
or  larger  firms,  and  partly  in  the  fact  that  only  thus  does  there 
arise  a  sufficiently  large  demand  for  many  goods.  This  large  demand 
has  two  causes,  the  size  of  the  urban  population  and  of  the  demand 
of  individuals  for  individual  goods  which  may  amount  to  three 
times  what  it  would  be  with  an  evenly  distributed  population.  This 
will  be  shown  later. 

2.    Chance  Agglomeration 

The  pattern  of  the  ideal  economic  region  will  show  that  location 
of  different  enterprises  may  coincide  even  when  they  derive  no 
advantage  at  all  from  one  another;  when  from  their  standpoint  the 
coincidence  is  merely  fortuitous.  Seen  from  the  standpoint  of  the 
regional  system  this  agglomeration  has  three  important  causes:  (1) 
orientation  by  a  capital  city,  (2)  orientation  by  main  roads,  (3)  the 
relative  distances  of  similar  locations  from  one  another.  These  rela- 
tionships, which  rest  on  the  original  distances  between  the  original 
settlements,  are  such  that  only  compartively  few  places  offer  possible 


include  their  followers:  handicrafts,  service,  trades,  etc.  But  this  is  a  very  rough 
approximation  only,  which  neglects  reactions  on  allegedly  independent  locations. 
Nevertheless  it  is  useful  in  planning  the  development  of  new  areas. 

15.  This  plays  an  important  role,  also,  in  the  development  of  a  downtown  district 
(a  "  city  ") ,  which  in  general  arises  for  essentially  the  same  reasons  as  do  towns  and 
particularly  capital  cities  within  a  country. 


78 


Part  One.     Location 


locations  for  industrial  enterprises,  which,  therefore,  necessarily 
gather  at  these  points,  especially  where  orientation  by  a  capital  city 
is  added.  Finally,  the  order  of  the  regional  system  creates  certain 
favored  points,  points  where  communication  routes  cross,  that  offer 
special  advantages  to  different  enterprises  independently  of  one 
another. 

8.  Agglomeration  of  Pure  Consumers  ^^ 
Corresponding  to  large  single  producers,  there  are  large  single 
consumers:  royal  courts  and  bishops'  sees  in  earlier  times,  garrisons 
and  administrative  and  educational  centers  today.  The  fact  that 
certain  institutions  like  fire  departments,  churches,  schools,  and 
places  of  entertainment  pay,  causes  pure  consumers,  also,  to  collect 
in  one  place.  This  agglomeration  of  consumers  is  further  favored 
by  the  advantages  of  association  and  situation.  In  short,  almost  all 
the  reasons  for  the  establishment  of  towns  by  producers  are  repeated. 

€.  Summary 
Even  though  the  earth  were  a  smooth  and  uniform  sphere  towns 
would  still  arise  for  numerous  reasons.  These  agglomerations  of 
locations  would  be  partly  fortuitous,  when  seen  from  the  standpoint 
of  those  concerned  though  not  from  the  standpoint  of  all,  and  partly 
the  result  of  advantages  they  offered  not  from  the  participants.  The 
advantages  are  divided  into  those  of  number  and  association,"  and 
of  site  and  supply.  All  may  be  subdivided  into  advantages  of  con- 
sumption, of  sales,  and  of  production.  The  latter  divide  into  advan- 
tages of  uniform  and  differentiated  production,  and  finally  into 
internal  and  external  economies.  At  first  all  these  factors  favoring 
the  establishment  of  towns  act  everywhere,  but  they  concentrate  at 
definite  points  as  soon  as  the  capital  and  the  main  highways  are 
located.  Under  our  assumptions,  these  may  be  located  arbitrarily, 
at  least  in  a  single  economic  region.  But  once  they  have  been  fixed 
whether  because  of  a  historic  advantage  or  by  political  act,  there  is 
no  further  room  for  arbitrariness  as  to  where  and  why  additional 
towns  shall  arise.  Thus  the  general  interdependence  among  all 
locations  determines  not  only  those  points  where  the  advantages  of 
site  suffice  for  agglomeration,  but  also  where  the  other  factors  men- 
tioned shall,create  towns,  either  singly  or  in  co-operation. 


16.  According  to  Sombart    (op.  cit.,  p.    142)    most   towns  were  consumers   in    the 
Middle  Ages,  whereas  today  they  are,  without  doubt,  chiefly  producers. 

17.  Of  course  the  advantages  of  number  and  association   include  those  of  site  as 
well,  but  are  not  exhausted  by  these. 


Reasons  for  Town  Settlement  79 

§2.     Restricted   Agglomeration    of  Location 
(The   Historical   System) 

We  have  mentioned  four  factors  besides  chance  that  always 
determine  the  establishment  of  towns:  numbers  and  association, 
site  and  supply.  The  latter  does  so  only  in  the  sense  that  it  appears 
first  during  locational  development,  and  then  in  turn  attracts  other 
enterprises.  Historical  reality,  with  its  spatial  differences  in  popu- 
lation density,  topography,  and  natural  resources  adds  another  factor 
that  operates  only  from  an  already  determined  place:  the  traditional 
source  of  supply.  This  concept  must  be  defined  in  a  wide  sense.  For 
producers  proper  it  may  include  raw  materials,  water  power,  a  favor- 
able climate,  or  labor  or  capital  that  are  already  available.  For 
transport  it  may  mean  a  river  valley  as  well  as  a  river  crossing;  for 
the  consumer,  climate  and  surroundings.  This  raises  no  new  prob- 
lems. We  have  already  learned  from  the  discussion  of  the  natural 
system  of  town  formation  that  certain  places  may  offer  special 
advantages.  The  field  to  which  this  applies  is  now  simply  widened 
considerably.  The  difference  is  merely  that  under  the  natural 
system  favored  places  do  not  appear  until  a  location  has  been  deter- 
mined, whereas  here  intrinsic  sources  of  supply  are  present  first. 
In  general  such  sources  of  supply  limit  the  number  of  possible 
locations  for  a  particular  industry,  but  increase  it  for  towns  since 
the  fortuitous  coincidence  of  locations  that  is  so  important  in  the 
natural  system  is  made  more  difficult. 

It  might  be  thought  at  first  that  site,  too,  is  one  of  the  historical 
factors.  Closer  scrutiny  shows,  however,  that  all  the  advantages  of  a 
historical  site  can  be  reduced  either  to  those  of  the  site  itself  or  to 
those  of  a  source  of  supply.  Neither  geologic  nor  geographic  dif- 
ferences of  any  sort  are  necessary  to  create  differences  in  the  favor- 
ability  of  a  site,  or  even  to  introduce  site  as  a  new  factor.  All  that  is 
new  is,  that  in  addition  to  location  on  the  basis  of  consumers, 
manufacturers,  and  routes  of  communication,  we  have  also  location 
on  the  basis  of  sources  of  supply. 

The  great  significance  of  these  in  the  establishment  of  towns  is 
this:  they  not  only  influence  the  location  of  rural  towns  and  high- 
ways, but  also  determine  that  of  the  capital  city  and  the  main  lines 
of  communication,  which  in  the  natural  system  was  left  to  free 
choice.  Differences  in  the  earth's  surface  ordain  from  the  very 
beginning  that  for  every  town  there  is  only  one  best  site.  They 
exclude  all  human  arbitrariness  in  so  far  as  it  is  unwilling  to  pay 


go  Part  One.     Location 

the  price.    But  Part  III  will  show  that  deliberate  intervention  may 
still  be  advisable. 

b.     THE    SITE    OF    TOWN    FORMATION 

§1.     Location    of   the  Individual   Town 

He  who  wishes  to  explain  or  determine  the  location  of  towns 
must  constantly  bear  in  mind  two  circumstances  above  all.  First, 
all  five  reasons  for  their  origin  determine  in  general  the  place  of 
their  settlement:  numbers  and  association,  site  and  supply,  and 
chance.  These  may  work  with  or  against  one  another.  Only  in  rare 
cases  will  one  factor  alone  be  decisive.  Second,  towns  as  a  rule  are 
not  merely  agglomerations  of  locations  of  similar  types,  but  above 
all  of  different  ones.  Thus  the  explanation  will  necessarily  differ 
with  the  branch  of  industry  or  the  kind  of  pure  consumer. 

a.    General  Determination  of  Site 

The  problem  of  location  for  the  individual  town  is:  Given  all 
other  towns,  to  find  a  site  for  this  one.  This  is  more  difficult  by 
far  than  to  determine  a  location  for  a  firm.  For  in  the  case  of  a 
town  not  only  one  but  many  locations  are  simultaneously  variable. 
Furthermore,  they  are  interdependent,  so  that  the  problem  cannot 
simply  be  reduced  to  that  other  one:  To  determine  the  location 
separately  for  each  industry  in  this  part  of  the  country,  on  the 
assumption  that  the  town  will  arise  where  many  of  these  locations 
approximately  coincide.  This  might  be  acceptable,  at  best,  as  a 
very  rough  first  approximation.  A  more  precise  analysis,  in  so  far 
as  economic  considerations  play  any  role  at  all,^^  cannot  possibly 
disregard  the  interdependence  of  the  locations  of  the  various  indus- 
tries concerned.  For  example,  each  individual  location  within  the 
area  under  examination  may  be  favorable  for  a  factory  in  different 
degree,  depending  on  the  exact  site  of  the  railway  station.  But  the 
site  of  the  latter  depends  again  on  the  location  of  all  the  other 
industries  in  the  district. 

A  somewhat  more  exact  statement  of  the  problem  consists,  there- 
fore, in  selecting  a  location  for  each  industry  for  every  possible 
combination  of  the  other  locations,  and  then  choosing  that  site  for 
the  town  in  whose  neighborhood  most  optimum  locations  (inter- 
dependence having  been  considered)    are  situated.    Even  this  state- 

18.  Obviously  they  do  not  in  the  case  of  fortresses,  administrative  or  religious 
centers,  and  the  like. 


Reasons  for  Town  Settlenieyit 


81 


merit  would  still  admit  arbitrary  selection  of  locations  that  are  not 
economically  determined,  but  nevertheless  economically  significant. 
This  problem  is  practically  insoluble. 

Thus,  as  in  choosing  a  location  tor  a  single  factory,  nothing 
remains  but  to  calculate  roughly  which  among  a  few  hypothetical 
sites  for  the  town  would  attract  most  industries.  The  best  that 
location  theory  can  do  is  to  suggest  the  locations  to  be  examined. 
Important  sources  of  supply,  intersections  of  traffic  routes,  and  the 
center  of  gravity  of  the  polygon  formed  by  the  neighboring  towns 
of  similar  function  are  such  test  locations.  But  one  should  not  be 
deceived  as  to  the  gross  inaccuracy  of  such  a  procedure.  Even  the 
excellent  rule  to  fix  the  site  of  a  town  first  in  the  economy  as  a 
whole,  then  within  a  region,"'2°  and  finally  at  the  place  itself  ^^  does 
not  usually  help  very  much.  For  these  three  situations  are  of  varying 
significance  for  different  industries,  and  the  advantages  of  one  may 
compensate  for  the  disadvantages  of  the  others. 

Thus  we  cannot  avoid  the  fundamental  difficulty  in  locating  a 
town:  We  can  neither  neglect  the  interdependence  of  the  locations 
of  the  firms  directly  concerned  nor  can  we  grasp  it  in  its  complexity. 
Even  after  exhaustive  examination  towns  continue  to  be  founded 
with  fingers  crossed,  and  the  reason  for  the  relatively  small  number 
of  failures  is  the  stickiness  of  the  location  system.  The  competition 
among  possible  locations  is  worse  than  imperfect.  In  earlier  times, 
and  particularly  during  the  critical  periods  of  first  development, 
it  was  still  further  restricted  by  state  privileges  or  municipal 
prohibitions. 

^.   Special  Cases 

Easiest  to  explain  is  the  location  of  a  town  at  a  favorable  point, 
which  in  this  context  means  in  particular  natural  resources,  loca- 
tions of  pure  large-scale  consumers,  and  intersections  of  traffic  routes. 
But  again  one  must  beware  of  regarding  such  obvious  advantages 
as  sufficient  causes  of  an  agglomeration  of  locations.  If  the  splendid 
port  of  New  York,  for  example,  were  on  a  remote  island  the  city 
would  consist  of  a  few  huts  at  the  best  and  one  of  the  competing 
ports,  Boston  or  Baltimore,  would  take  its  place;  or  if  necessary  an 
artificial  harbor  would  be  built. -^   On  the  other  hand,  if  the  whole 

19.  More  exactly,  in  the  area  enclosed  by  neighboring  towns  of  similar  function. 

20.  For  a  short  description  of  all  German  towns  see  E.  Keyser,  ed.,  Deutsches 
Stddtebuch    (Stuttgart,  1939  and  following  years)  . 

21.  E.  A.  Kautz  has  minutely  analyzed  the  limited  significance  of  a  natural  coastal 
situation  for  the  location  of  seaports  in  Das  Standortproblem  der  Seehdfen  (Jena, 
1934) ,  pp.  15,  33,  and  elsewhere. 


82  Part  One.    Location 

East  Coast  hinterland  were  a  desert,  New  Orleans  or  San  Francisco 
would  flourish  despite  the  splendid  Atlantic  harbors.  It  might  be 
mentioned  incidentally  that  a  good  part  of  the  business  of  New  York 
has  been  directly  attracted  neither  by  such  advantages  of  site  as  its 
harbor  and  the  rock  foundation  for  skyscrapers,  nor  by  its  closer 
proximity  to  American  and  West  European  industrial  areas  than 
any  of  the  more  southerly  ports,  nor  by  its  situation  at  the  terminus 
of  the  Erie  Canal  and  of  many  railroads,  etc.,  but  by  the  advantages 
of  numbers. 

Consider  first  a  few  examples  of  cities  whose  existence  seems  to 
have  been  determined  to  a  high  degree  by  their  location.  The 
centers  of  states  or  of  natural  basins  often  have  the  advantage  of 
being  optimum  transport  points  in  a  region  that  cannot  easily  be 
reduced  by  outside  competition  because  it  is  protected  by  natural 
or  artificial  tariff  walls.  Such  points  are  ideal  locations  for  con- 
sumption-oriented industries  ^^  with  an  extended  sales  radius. 

Leipzig,  for  example,  possesses  this  advantage  in  double  measure: 
It  is  the  approximate  center  of  the  basin  that  is  bounded  by  the 
Erzgebirge  range,  the  Thuringian  Mountains,  and  the  Harz  Moun- 
tains, all  about  sixty  miles  distant.  It  is  also  the  central  city  of 
Germany;  almost  all  of  Germany  lies  within  two  hundred  and  fifty 
miles  of  Leipzig,  or  a  comfortable  day's  journey,  and  conversely, 
nearly  the  entire  area  within  that  radius  is  German.  A  third  advan- 
tage of  its  location  is  that  the  Berlin-Munich,  Upper  Silesia-Ruhr, 
and  Hamburg-Prague-Vienna  trunk  lines  intersect  there. 

Chicago  possesses  similar  advantages.  True,  it  does  not  lie  at  the 
center  of  the  United  States,  but,  more  important,  considering  the 
unequal  distribution  of  the  population,  it  is  near  the  center  of 
population  and  production  (measured  by  "  value  added ") .  In 
addition,  there  is  its  unique  situation  where  the  railway  between 
New  York  and  Minneapolis  meets  the  steamship  lines  on  the  Great 
Lakes;  and,  less  important,  between  the  iron  mines  near  Lakes 
Superior  and  Michigan  and  the  coal  of  Pennsylvania.  Paris,  too, 
belongs  in  this  group  as  center  of  the  basin  named  after  it,  as  do 
Breslau,  Prague,  Frankfort  (midway  between  the  most  important 
European  capitals  and  banking  centers) ,  and  the  encircled  Addis 
Ababa  and  Madrid.  The  latter,  though  in  the  geographic  center 
of  Spain,  lies  away  from  the  center  of  population  and  industry. 

Places  favored  in  another  way  by  location  are  those  where  traffic 

22.  Industries,  that  is,  in  which  location  with  respect  to  consumers  is  important. 

23.  On  towns  arising  through  damming  of  traffic  see  F.  Ratzel.  "  Die  geographische 
Lage  der  grosen  Stadte,"  Kleine  Schriften,  II,  446. 


Reasons  for  Town  Settlement  83 

is  dammed  up  by  transshipment.^^  Points,  that  is,  where  lines  of 
communication  cross  (pure  situation) ,  or  traffic  lines  of  different 
sort  meet  (situation  at  sources  of  supply  as  on  a  seacoast) .  Hamburg 
and  Cologne  owe  much  to  this. 

But  the  most  significant  special  cases  are  those  where  choice  of 
location  is  restricted  by  a  source  of  supply.  More  important  still 
than  localities  that  are  favorable  to  traffic,  such  as  harbors,  are  those 
to  which  production  must  conform:  above  all  sources  of  coal,  a 
material  that  loses  much  weight  in  production.  Since  coal  sup- 
planted wood  in  smelting  and  ore  has  moved  toward  coal,^*  and 
since  the  substitution  of  steam  for  water  power,  favorably  situated 
coal  fields  have  become  prominent  among  those  regions  that  are 
studded  with  towns.  Take,  for  example,  England,  where  nearly 
all  the  large  cities  are  concentrated  in  the  coal  districts,  or  the  highly 
urbanized  zone  stretching  from  the  coal  of  northern  France  and 
Belgium  across  the  Ruhr  and  the  lignite  region  through  Upper 
Silesia  and  far  on  into  Poland.^^  Examples  of  source-oriented  con- 
sumption are  health  resorts,  many  university  towns,  religious  shrines, 
and  capitals. 

But  not  much  is  proved  by  such  examples.  Dependence  on  source 
does  not  mean  unconditional  restriction  to  a  source,  still  less  to  one 
particular  source;  for  competing  sources  and  other  factors  which 
affect  town  formation  become  relevant.  Neither  does  it  mean  that 
all  of  the  industries  of  a  town  are  confined  to  this  one  source.  Some 
are  tied  to  the  source  of  supply,  since  they  depend  in  turn  upon 
industries  that  are  so  tied.  Others,  however,  find  themselves  in  the 
town  although  not  one  of  the  forces  that  determine  their  location 
has  its  seat  there.  The  site  of  a  town  can  be  explained  satisfactorily 
in  the  end  only  by  calculating  its  advantages  over  competing  sites. 
This  becomes  even  more  obvious  if  the  problem  is  to  find  the  most 
advantageous  location,  not  to  explain  its  actual  location,  which  is 
so  often  determined  by  past  and  fortuitous  conditions. 


24.  Improvements  in  the  technique  of  smelting  have  undermined  this  rule  however, 
because  the  amount  of  coal  required  per  unit  of  iron  has  been  reduced.  Furthermore, 
ore  deposits  have  become  more  and  more  powerful  locational  attractions,  as  ores  with 
less  and  less  iron  content  have  to  be  used. 

25.  The  concentration  of  towns  in  Germany  would  have  been  even  greater  had  coal 
not  been  shipped  by  rail  over  great  distances,  probably  far  below  cost.  The  low  long- 
distance rates  for  coal  were  one  of  the  most  important  factors  in  location  and,  indeed, 
in  the  decentralization  of  former  times.  Electricity,  too,  which  is  cheaper  to  transport 
over  short  distances  than  coal,  has  recently  had  a  dispersive  effect. 


8^  Part  One.    Location 

§2.    The   System   of   Town   Locations 

As  towns  are  essentially  agglomerations  of  locations  of  economic 
activities,  the  system  of  town  locations  is  defined  simultaneously  by 
the  general  equations  of  location  and  the  geometry  of  economic 
regions,  which  will  be  discussed  later.  The  general  location  problem 
is  the  same  for  single  industries  and  agglomerations  of  industries. 
In  the  case  of  the  individual  plant  it  differs  only  because  fewer 
variables  need  be  considered  in  selecting  a  site  for  a  factory  than 
for  a  town. 


Chapter  7.     Site  and  Cause  of  Belt  Formation 


We  shall  limit  our  analysis  to  belt-shaped  areal  agglomeration 
of  locations  of  production   (see  pp.  10-11) . 

a.     BELTS   OF   LOCATIONS    PRODUCING   IDENTICAL   GOODS 

§1.     Advantages   of  Specialization 

Consider  the  cotton  belt,  the  corn  belt,  the  wheat  belt,  and  so 
on  in  the  United  States.  These  belts  produce  mainly  the  crop  m 
question;  or,  which  is  not  the  same  thing,  most  of  the  crop  in  ques- 
tion is  produced  there.  Belts  are  formed  for  the  same  reasons  as 
towns:  the  advantages  of  site,  source,  and  scale. 

Thiinen  showed  more  than  a  hundred  years  ago  how  different 
advantages  of  a  site  make  it  profitable  to  specialize  in  different  crops 
in  successive  zones  around  a  market,  and  here  it  will  suffice  merely 
to  recall  Chapter  5. 

Among  the  advantages  of  a  source  of  supply  we  included  a  special 
suitability  of  soil,  of  climate,^  and  of  population  for  the  production 
of  a  certain  commodity.  But  it  would  be  no  explanation  of  the 
cotton  belt,  for  example,  to  tell  how  its  natural  conditions  favor 
the  cultivation  of  "  white  gold."  They  might  favor  other  branches 
of  agriculture  as  well.  Certainly  it  is  not  only  here  that  cotton  can 
be  grown,  for  the  necessary  conditions  occur  elsewhere  too,  or  at 
least  could  be  provided;  for  example,  by  transplanting  cheap  Negro 
labor  from  the  cotton  belt.  Only  by  comparison  can  it  be  proved 
that  conditions  here  are  exactly  suited  to  the  cultivation  of  cotton. 
Of  course  mere  physical  yields  must  not  be  compared,  since  these 
depend  entirely  upon  input.  Where  but  one  crop  is  grown  only 
the  highest  profits  attainable  per  unit  of  area  are  really  comparable. 

Figure  18  provides  an  example.  The  profits  from  two  crops, 
1  and  2,  on  two  different  grades  of  soil,  I  and  II,  are  compared. 
The  technique  of  presentation  is  as  follows:  ^  Profit  is  greatest  where 

1.  Differences  in  climate  and  situation  determine  agricultural  location  chiefly  in  the 
large,  differences  in  soil  in  the  small.  See  T.  Brinkmann,  "  Die  Okonomik  des  land- 
wirtschaftlichen  Betriebs,"  Grundriss  der  Sozialokonomik    (1922) ,  Sec.  7,  p.  91. 

2.  After  A.  Haase,  "  Die  Thiinensche  Intensitatstheorie  in  graphischer  Darstellung," 
in  Thiinen  Festschrift,  edited  by  Seedorf  and  Seraphim    (Rostock,  1933)  ,  p.  202. 

85 


86 


Fart  One.     Location 


marginal  cost  equals  marginal  receipts.  Geometrically  this  means 
that  the  tangents  to  the  curves  for  receipts  and  cost  per  acre  must 
be  parallel.  Or,  since  in  the  example  the  cost  curve  is  a  straight 
line,  the  tangent  to  ei,  for  example  at  B,  must  simply  be  parallel  to  a. 
Then  gi  is  the  highest  profit  that  can  be  achieved  by  crop  1  on 
soil  I.  On  this  soil  gi  >  ga,  hence  cultivation  of  the  first  crop  will 
be  more  profitable,  whereas  the  second  will  be  more  profitable  on 
soil  11.^  If  nature  were  the  only  location  factor,  the  area  of  cultiva- 
tor crop  1  would  have  to  coincide  with  the  area  of  soil  I.* 


Cost  per  acre,  in  dollars 


Cost  per  acre,  in  dollars 


Fig.  18. 


Suitability  of  different  soils  for  different  products. 
a)  Cost  per  acre,  dollars; 

e)  receipts  per  acre  as  function  of  cost,  in  dollars; 
g)  profit  per  acre  as  function  of  cost,  in  dollars 
The  subscripts  refer  to  products  1  and  2  respectively. 


The  third  cause  for  the  establishment  of  belts  is  the  advantage 
of  numbers,  which  favors  regional  specialization  particularly  in 
staple  products  that  are  not  raised  for  local  need  only.  If  every 
farmer  in  the  United  States  were  to  devote  a  few  fields  to  cotton, 
assuming  that  climate  permitted,  the  cost  of  production  would  be 
considerably  increased.  To  begin  with  he  would  be  less  familiar 
with,  or  less  well  equipped  for,  cotton  growing,  or  at  least  his  equip- 
ment would  not  be  fully  used.  In  short,  the  scale  of  production 
would  be  too  small  on  the  individual  farm  and  production  costs 
would  rise  accordingly.  In  addition  there  would  be  disadvantages 
unconnected  with  the  individual  farm.    The  radius  of  the  supply 


3.  If  product  1  were  more  profitable  on  both  soils  the  situation  would  suggest 
application  of  the  theorem  of  comparative  costs.  We  shall  return  to  this  in  note  46 
on  p.  252. 

4.  The  figure  eliminates  the  influence  of  site  in  assuming  that  the  grower's  price 
is  the  same  everywhere.    On  pp.  87  f.  site  also  will  be  taken  into  consideration. 


Belt.  Formation  87 

area  for  cotton  gins  and  presses  would  have  to  be  considered  because 
of  the  small  return  in  raw  material  per  unit  of  area.  Thus  much 
higher  freight  costs  would  result.  The  whole  sales  organization 
would  be  more  diffuse  and  less  fully  used.  No  single  port  in  the 
country  would  ship  enough  bales  to  make  profitable  the  loading 
machinery  and  efficient  export  presses  that  now  exist  in  the  two 
southern  ports  specializing  in  the  shipment  of  cotton. 

Similarly,  every  other  belt  has  its  centers:  commodity  exchanges, 
transshipment  points,  collecting  stations,  sales  markets,  research  insti- 
tutes, and  so  on.  Other  things  being  equal,  profits  decrease  with 
distance  from  these  centers,  either  because  all  shipments  pass  through 
them,  or  because  with  increasing  distance  their  facilities  can  be 
enjoyed  only  with  correspondingly  greater  difficulty.  Thus  pro- 
duction crowds  around  these  centers,^  whose  existence  may  even 
depend  on  this  crowding.*' 

If  a  belt  has  several  such  centers  (and  the  competition  of  towns 
tends  to  maximize  their  number),  we  are,  depending  on  their  origin, 
not  confronted  by  only  one  homogeneous  belt.  Thus,  for  example, 
one  should  distinguish  the  cotton  districts  around  New  Orleans, 
around  Houston  and  Galveston,  and  around  a  few  smaller  ports. 
Of  course  this  does  not  prevent  the  cotton  belt,  as  far  as  the  other 
reasons  for  its  origin  are  concerned,  from  constituting  a  unit 
nevertheless. 

But  the  forces  which  work  toward  the  establishment  of  belts 
seldom  operate  without  interference.  Their  influence  is  partly 
cumulative,  partly  compensating.  A  single  example  may  suffice 
(see  Fig.  19) .  If  it  were  merely  a  question  of  site,  and  if  the  soil 
everywhere  were  thus  of  the  same  quality,  I,  product  I  would  be 
cultivated  about  the  point  O  up  to  the  distance  OC,  but  from 
there  on  up  to  OD  product  2  would  be  grown.  Now  suppose,  how- 
ever, that  from  A  outward  the  soil  is  of  quality  II,  more  favorable 
for  crop  2.  Besides  the  curves  for  the  profit  per  hectare  on  soil  I, 
gi^  and  g2^  we  must  draw  in  the  corresponding  curves  gi"  and  ga" 
for  soil  II.  For  product  1,  the  second  curve  lies  below  the  first;  for 
product  2,  above  it.    The  profits  per  hectare  are  now  equal  at  dis- 

5.  This  is  especially  true  of  small  enterprises,  which  depend  more  on  external 
economies  than  do  the  larger  ones. 

6.  This  would  be  represented  graphically  in  such  a  way  that  with  scattered  pro- 
duction the  demand  curve  for  the  services  of  a  center  would  not  even  touch  its  cost 
curve,  let  alone  intersect  it.  As  soon  as  production  is  spatially  concentrated,  however, 
the  demand  curve  will  be  rotated  upward  about  its  intersection  with  the  price  axis 
until  finally,  with  sufficient  concentration,  it  will  at  least  touch  the  cost  curve. 


88 


Part  One.     Location 


tance  OB,  and  B  necessarily  lies  between  A  and  C.  The  area  for 
cultivation  of  the  second  product  will  not  include  the  entire  area, 
II,  which  is  especially  suited  to  it,  yet  it  will  push  nearer  to  the 
market  than  it  could  if  only  distance  matteredJ'^ 


•  Crop  1 


Fig.  19.    Location  of  crops  as  a  function  of  soil  quality 
and  distance 


§2.     Disadvantages   of   Specialization 

There  are  forces  at  work,  however,  that  prevent  a  region  from 
specializing  in  one  product.  This  difficult  subject  has  already  been 
so  thoroughly  analyzed  that  a  brief  summary  will  suffice  for  the 


7.  Hence  the  suitability  of  a  location  is  decided  not  by  site  (quality  of  soil)  alone, 
but  also  by  situation  (producer's  price)  .  With  an  adequate  price  a  crop  will  be 
cultivated  even  on  less  suitable  soil.  A  good  example  is  the  enormous  increase  in 
conifer  plantations  at  the  expense  of  deciduous  trees  since  the  rise  of  industrialization. 
Fir  quickly  produces  the  desired  timber,  and  beechwood  has  been  supplanted  as  a 
fuel  by  the  cheaper  coal.  (See  H.  Koch  et.  ah,  Die  Buche  der  Ostalb.  Eine  Standort- 
untersuchung  [Stuttgart,  1939],  pp.  92  ff.)  We  have  entirely  disregarded  above  the  fact 
that  with  the  introduction  of  a  new  quality  of  soil  into  our  example  the  market  prices 
of  both  produ.cts  necessarily  change.  This  change  would  shift  point  B  somewhat 
farther  outward,  but  not  so  far  as  to  make  it  coincide  with  C. 

8.  Other  considerations,  of  course,  favor  the  cultivation  of  a  single  crop  in  the 
vicinity  of  a  town.  Here  predatory  cultivation  can  be  allowed  for  sooner  than  any- 
where else,  or  counteracted  with  expensive  fertilizers  instead  of  by  mixing  or  rotating 
crops  (see  Koch,  loc.  cit.,  for  forestry,  which  is  subject  to  the  same  laws  of  location  as 
agriculture) .  On  the  other  hand,  the  cultivation  of  one  crop  far  from  a  town  is  made 
possible  by  rotating  or  even  migrating  cultivation. 


Belt  Formation 


89 


present  purpose.   The  following  presentation  is  based  on  the  works 
of  F.  Aereboe  and  T.  Brinkmann.^ 

The  following  arguments  in  particular  speak  against  the  cultiva- 
tion of  a  single  crop:  (1)  It  makes  only  partial  use  of  the  soil,  and 
in  the  long  run  requires  a  greater  expenditure  of  fertilizer.  (2)  It 
leads  to  seasonal  peak  demands  for  labor,  which  can  be  overcome 
only  by  an  increase  in  wages.  (3)  It  stakes  everything  on  one 
venture;  the  more  economically  self-sufficient  a  farm  is,  the  less 
sensitive  is  it  to  fluctuations  in  costs  and  selling  prices  and  the  more 
easily  can  it  adapt  itself  to  permanent  structural  changes  in  the 
market.  (4)  It  raises  freight  costs.  (5)  Moreover,  strict  specializa- 
tion in  one  product  is  often  technically  impossible.  Thus  where 
wool  is  produced,  mutton  also  is  obtained;  where  manuring  is 
required,  fodder  must  be  raised,  and  so  on.  For  these  various  reasons 
a  point  is  inevitably  reached  where  the  lowered  costs  due  to 
increasing  mass  production  are  outstripped  by  the  rising  costs  due 
to  increasing  specialization. 

The  resultant  of  the  forces  working  toward  specialization  and 
diversification  is  a  compromise.  It  is  not  the  commodity  that  may 
appear  at  first  sight  to  yield  the  greatest  profit  that  is  produced,  but 
rather  that  combination  of  a  limited  number  of  goods  that  will 
turn  out  to  be  the  most  profitable  in  the  long  run.  In  general,  but 
particularly  far  from  a  market  where  only  a  few  crops  may  eco- 
nomically be  chosen,"  the  combination  will  include,  or,  rather  prefer 
products  that,  considered  singly  for  the  short  run,  can  be  cultivated 
with  greatest  profit.  But  this  is  not  absolutely  certain.  It  is  impos- 
sible to  offer  a  more  concrete  theoretical  rule  for  determining  the 
optimum  combination  than  this  general  statement.  From  the  innu- 
merable possible  combinations  "  the  one  that  affords  the  greatest 
possible  average  profit  throughout  the  planning  period  will  be 
chosen. 

Because  of  the  frequent  interdependence  of  marginal  revenues 
this  does  not  necessarily  presume  that  for  every  single  product  in 
the  combination  marginal  costs  equals  marginal  revenue,  but  only 
that  none  of  the  many  possible  and  infinitely  small  changes  in  the 
combination,  embracing  several  products  at  the  same  time,  will 
yield  an  additional  profit. 

9.  F.  Aereboe,  Kleine  Landwirtschaftliche  Betriebslehre    (Berlin,  1932) . 

T.  Brinkmann,  "  Bodennutzungssysteme,"  Handworterbuch  der  Staatswissenschaften, 
4th  ed..  Vol.  II;  "  Die  Okonomik  des  landwirtschaftlichen  Betriebs,"  Grundriss  der 
Sozialokonomik,  1922)  ,  Sec.  7,  pp.  27-124. 

10.  See  p.  88,  note  8. 

11.  This  does  not  mean  that  any  combination  is  possible. 


90 


Part  One.     Location 


Finally,  it  may  be  concluded  that  although  the  disadvantages  of 
specialization  do  not  actually  prevent  the  formation  of  belts,  never- 
theless they  prevent  the  production  in  these  belts  of  only  the  single 
commodity  whose  name  they  bear. 

b.     BELTS    OF    DIFFERENT    LOCATIONS 

The  areal  agglomeration  of  different  locations,  which  may  be 
illustrated  by  industrial  districts,  has  essentially  the  same  causes  that 
we  have  already  encountered  so  frequently;  the  advantages  of  site 
and  source  of  supplies,  of  scale  and  association.  The  advantages  of  site 
brings  about  industrial  agglomerations  independently  of  all  natural 
inequalities.  Even  in  the  ideal  economic  district,  as  will  be  seen 
later,  there  are  sectors  that  are  especially  rich  in  towns,  because 
the  main  lines  of  communication  can  thus  be  used  to  best  advantage. 
In  the  actual  economy  there  are  the  additional  advantages  of  situa- 
tion at  a  source  of  supply  and,  above  all,  of  these  sources  themselves. 
As  the  weight  of  coal  does  not  appear  in  the  finished  product,  coal 
fields  are  especially  attractive  to  industry.  It  has  already  been 
pointed  out  that  up  to  the  World  Wars  almost  all  the  large  towns 
in  England,  with  the  exception  of  her  seaports,  lay  in  one  of  the 
coal  regions. 

Especially  fertile  soils  also  may  attract  industry,  for  a  dense 
agricultural  population  offers  a  good  location  for  enterprises  that 
are  strongly  consumer  oriented.  Climate,  too,  plays  no  small  role. 
Thus  the  northerly  and  southerly  limits  of  the  North  American 
industrial  belt  were  undoubtedly  fixed  in  part  by  the  fact  that  the 
climate  beyond  them  was  too  strange  to  northwest  Europeans,  who 
composed  the  bulk  of  the  immigation  and  of  the  industrial  popu- 
lation up  to  the  end  of  the  nineteenth  century.  Similarly,  the 
ancient  Greek  colonization  appears  to  have  been  restricted  to  a 
climatically  uniform  region.^^  But  even  more  striking  is  the  intense 
agglomeration  of  populations  along  the  seacoasts  in  antiquity, 
which  resulted  fiom  the  advantages  of  site  and  sources  of  supply. 
According  to  Gillman  ^*  colonization  in  Africa  depended  critically 
upon  water  supply.  Not  least  in  importance  are  the  locations  of 
men  with  special  gifts,  since  the  most  favorable  environments  for 
industries  is  found  in  those  places  where  an  unusual  intellectual 
activity  has  developed. 

12.  J.  H.  Schultze,  "  Zur  Geographic  der  altgriechischen  Kolonisation,"  Peterm. 
Mitteilungen,  LXXXVII   (1941),  7-12.   With  a  map. 

13.  Geographic  Review    (1936). 


Belt  Formation  91 

The  advantages  of  size  and  scale  of  production,  finally,  are  like- 
wise obvious.  The  more  industrial  production  exceeds  agricultural, 
the  more  do  the  same  causes  underlying  the  establishment  of  a  city 
in  an  ideal  system  favor  the  development  of  industrial  areas,  which, 
because  of  the  cost  of  land,  transportation,  and  labor  are  often  merely 
sprawling  cities.  But  just  as  we  found  it  impossible  to  offer  more 
than  a  very  general  formula  for  a  system  of  agricultural  enterprises, 
so  one  should  not  expect  a  demonstration  of  how  the  location  of 
industrial  areas  must  necessarily  be  determined.  There  are  usually 
plausible  reasons  in  favor  of  certain  regions,  of  course,  and  the 
better  we  know  the  possible  factors  and  their  effects  the  more  cer- 
tain it  is  that  none  of  the  factors  operating  in  individual  cases  will 
be  overlooked. 


Chapter  8.     The  Problem  of  General  Location  Patterns 


Certainly  it  is  more  than  a  mere  coincidence  that  the  theory  of 
economic  location  has  been  almost  entirely  confined  so  far  to  the 
point  of  view  of  the  individual  firm.^  As  in  price  theory,  the  inter- 
dependence of  all  economic  events  was  eliminated  by  simplifying 
assumptions,  and  the  problem  thus  made  susceptible  of  geometric 
treatment.  But  in  contradistinction  to  price  theory,  the  proof  of  the 
existence  of  a  general  equilibrium  and  of  its  conditions  is  of  far 
less  interest  here.  After  the  Walrasian  equations  had  confirmed  the 
belief  of  the  Enlightenment  that  even  an  economy  given  over  to 
competition  will  hover  in  equilibrium,^  nothing  fundamentally  new 
seemed  to  have  been  added  when  this  proof  was  complicated  by  the 
introduction  of  space  and  time.  Later,  when  many  had  entirely 
abandoned  that  belief,  there  seemed  on  the  other  hand  to  be  little 
sense  in  trying  to  prove  for  the  particular  what  they  had  long  been 
unable  to  see  in  the  general:  that  there  is  a  reason  in  things  pre- 
serving them  from  chaos,  and  as  a  rule  without  any  human  assis- 

1.  Alfred  Weber  {Ueber  den  Standort  der  Industrien,  P.  I  [Tubingen,  1909],  pp. 
200  ff.)  has  already  described  the  reciprocal  effect  between  the  locations  of  various 
branches  of  the  economy.  He  distinguished  strata  according  to  whether,  like  agriculture 
as  the  basic  layer,  they  were  more  influencing  or,  like  "  central  organizers  "  as  the 
uppermost  stratum,  more  influenced.  According  to  Predohl  ("  Das  Standortproblem  in 
der  Wirtschaftstheorie,"  Weltwirtschaftliches  Archiv,  XXI  [1925],  304)  the  systems  of 
equations  that  determine  the  prices  and  distribution  of  production  factors  with  respect 
to  interdependence  implicitly  solve  also  the  problem  of  location.  E.  Schneider  ("  Preis- 
bildung  und  Preispolitik  unter  Beriicksichtigung  der  geographischen  Verteilung  von 
Erzeugern  und  Verbrauchern,"  Schmollers  Jahrbuch  [1934])  set  up  price  equations 
which  take  account  of  all  locations.  But  all  of  them  merely  touch  the  problem: 
Weber's  description  has  less  application  where  the  agricultural  sector  is  smaller,  as  in 
rich  countries  or  in  those  that  import  their  food;  and  his  explanation  selects  only  one 
factor:  the  influence  of  locations  for  consumption.  Predohl  treats  actually  only  the 
problem  of  individual  economic  units,  and  Schneider  assumes  locations  as  given  from 
the  first. 

2.  It  seems  to  me  the  chief  contribution  of  classical  and  neoclassical  theory  to  have 
proved  on  a  simple  model— no  one  can  take  everything  into  consideration— that  when 
certain  assumptions  are  guaranteed  a  free  economy  will  work.  Whether  it  will  work 
in  a  desirable  manner  is  another  question,  and  here  the  classical  proofs  are  no  longer 
convincing.  But  such  reflections  must  not  shake  our  belief  in  the  fundamental  impor- 
tance of  the  contribution  just  mentioned. 

92 


General  Location  Patterns  93 

tance  whatsoever.  Once  the  self-confidence  of  thinking  men  that 
culminated  in  Hegel  had  been  destroyed,  the  world  founded  on  it 
was  put  out  of  joint  socially,  politically,  and  economically  in  turn. 
Because  of  his  lack  of  belief  in  a  pre-established  harmony  man 
believed  that  he  himself  must  set  things  in  order;  but  the  more 
eagerly  he  went  about  it  and  the  more  planlessly  he  acted  in  oppo- 
sition to  the  conditions  of  that  harmony,  the  more  surely  was  it 
destroyed.  Today,  when  we  are  sensitive  once  more  to  the  natural 
rhythm,  it  seems  time  to  ask  who,  or  what,  really  failed  in  the 
economic  sphere  during  the  years  of  decline:  the  rational  and  there- 
fore natural  order— or  we? 

It  is  not  true  that  man  must  supply  the  world  with  an  organizing 
principle!  It  already  exists,  though  in  human  relations  it  functions 
unconditionally  just  as  little  as  man  acts  morally  of  himself.  The 
natural  equilibrium  of  economics  differs  from  the  equilibrium  of 
nature  exactly  as  the  moral  differs  from  the  mechanical.  Nature 
works  according  to  laws,  but  man  acts  according  to  his  idea  of  laws. 
In  other  words,  nature  must,  man  may,  act  correctly.  In  order  to 
do  so  he  must  have  some  conception  of  how  he  shall  act.  As  to 
economic  equilibrium  this  means  that  in  order  to  guide  his  activities 
he  needs  insight  into  the  conditions  of  this  equilibrium.  This  is 
especially  true  for  the  lawmaker,  since  all  others  are  bound  by  his 
precepts  even  though  unable  to  perceive  their  rationality.  What 
matters  is  that  statesmen  shall  act  correctly;  the  comforting  assurance 
that  all  will  come  right  of  itself  is  no  longer  granted  us.  Actually 
they  need  plan  little,  but  it  is  essential  that  this  little  be  planned 
with  enconomic  insight.^  Knowledge  of  the  conditions  governing 
the  most  general  equilibrium  is  not  enough  today;  it  is  necessary  to 
know  also  how  it  works  under  conditions  that  are  more  nearly 
real.  It  is  for  this  reason  that  time  and  space  can  no  longer  be 
neglected. 

The  following  paragraphs  will  discuss  the  conditions  of  general 
equilibrium  in  space.* 


3.  The  few  great  simple  principles  according  to  which  the  economy  works  basically, 
and  the  few  more  according  to  which  it  works  desirably  must  be  strictly  observed 
of  course;  then  there  will  seldom  be  need  of  interfering  in  details.  This  is  the 
meaningful  sythesis  of  restraint  and  freedom. 

4.  The  center  of  gravity  of  theoretical  economics  is  shifting  once  more:  Emphasis 
was  laid  at  first  on  a  price  theory  that  neglected  time  and  space;  then  the  theories  of 
interest  and  business  cycles  introduced  time;  and  now  the  third  period  has  dawned, 
when  space  is  seriously  considered. 


94 


Part  One.     Location 


a.     THE    EQUILIBRIUM    OF    LOCATIONS 

This  is  determined  by  two  fundamental  tendencies:  the  tendency 
as  seen  from  the  standpoint  of  the  individual  firm  and  hitherto 
alone  considered,  to  the  maximization  of  advantages;  and,  as  seen 
from  the  standpoint  of  the  economy  as  a  whole,  the  tendency  to 
maximization  of  the  number  of  independent  economic  units.  The 
latter  is  affected  by  competition  from  without,  the  former  by  indus- 
trial struggle  within.  The  individual  chooses  his  location  in  such 
a  way  as  to  athieve  the  highest  profit  as  a  producer,  or  the  cheapest 
market  as  a  consumer.  But  in  so  doing,  as  though  it  were  a  trick  of 
the  idea,  he  makes  possible  the  existence  of  more  competitors.  They 
crowd  into  the  market  and  reduce  his  living  space  until  his  advantage 
disappears.  There  is  constant  struggle  between  two  forces;  what  is 
gained  by  the  one  is  taken  back  again  by  the  other. 

The  point  where  these  forces  balance  determines  location.  This 
equilibrium,  born  of  the  interdependence  of  locations,  can  be  under- 
stood only  through  a  system  of  general  equations  of  location.  As 
soon  as  the  conditions  expressed  by  these  equations  have  been  ful- 
filled the  struggle  for  space  dies  down,  and  when  the  equations  are 
solved  the  locations  themselves  are  determined. 

We  now  present  the  general  conditions  of  equilibrium  that  are 
valid  for  independent  producers  and  consumers,  for  agriculture  as 
well  as  for  industry,  and  develop  the  pertinent  equations  briefly  for 
the  latter   (Tables  3  and  4)  .^ 

Condition  1:  The  location  for  an  individual  must  be  as  advan- 
tageous as  possible.  An  entrepreneur  therefore  makes  his  choice 
within  the  whole  district  and  within  his  market  area  in  such  a  way 
that  his  profit,  within  the  narrow  limits  still  left  by  the  general 
interdependence  within  the  economy,  shall  be  greatest.*'  With  the 
same  purpose  in  mind  the  farmer  decides  where  he  shall  buy  land, 
and  where  he  shall  place  his  buildings  on  it.  Consumers  select  a 
location  in  accordance  with  the  same  principle. 

5.  In  order  to  eliminate  all  extra-economic  factors  for  the  time  being  we  assume 
that  industrial  raw  materials  are  evenly  distributed  over  a  wide  plain,  in  which  the 
agricultural  population  also  is  evenly  distributed  and  lives  in  a  similar  fashion.  All 
industries  and  their  production  methods  are  assumed  to  be  accessible  to  everyone.  This 
simplifies  the  equations,  yet  alters  nothing  in  the  conditions  that  they  formulate. 

6.  If  all  locations  but  one  are  thought  of  as  given,  everything  in  the  equation 
for  S"»,  Table  3,  is  constant  except  the  coordinates  (x»»,  y"^) .  The  partial  derivatives 
with  respect  to  them  then  hold  the  condition  that  the  location  p"*  will  be  chosen  at 
the  point  of  greatest  profit    (equation  1 ,  Table  4) . 


General  Location  Patterns 


95 


Table  3.    SYMBOLS   OF   SPATIAL   ARRANGEMENT 


Product 

No. 

Place  of  Production 

Market  Boundaries 

Site 

Number 

Abbreviations  of  their 
equations 

Number 

1 
2 

m 

p1  (x}  y});  Pj  .    . 
Pf  (xfyr);Pi  .     . 

■  Pi 

a 
b 

ai,  Pi   .      .    ej,  a2,  P2    •      . 

2    „2              2      2    „2 
ai,  ^1   .      .  jji;  a2,  ^2  •      • 

A 
B 

Q 

PrCx^yH     ■    • 

K 

ai  ,  Pi      .      .  dj  ;  a2  ,  P2 

m 

(Together) 

n 

2a  +  b  4 

(Together) 

N 

= 

-•q|                 |=2A+B  +  .Q 

2 

•    Given 

■ 

d"'  =  /'"(n")     Individual  demand  for  product  m 

'^  ^  —  V   {    <i)      •    •      V  j  Qf  pioduct  m  at  site  q  as  a  function  of  the  total 

,^  ,  Average  cost  ^  ,  ,  „ 

j^m  ^     m/£)  \        t         A     .■  \  demand  D"*  =  )i'(f'»,x"y"',a'"fl'"  •  •  e'",o-,  (7"  •  •') 

1       -^   ^    "^  of  production  J  <i        "^v     .,,;,.     q^q  q'"'"*       /• 

S"*  =  D"  •  (tt™  —  k"")     Profit  on  product  m  at  site  q 

a     Rural  population  per  sq.  km. 

0-"  Urban  population  of  the  town  P"" 

r     Freight  rate 

m     Number  of  products 

G     Size  of  entire  area 


•    To  find 

1.  tt""  Factory  price  of  product  m  at  location  P'J 

2.  G™  Sales  area  of  location  p"  in  sq.  km. 

3.  q™  No.  of  towns  that  produce  product  m 

4.  X™,  y™  Coordinates  of  location  P'" 

5.  a™,  /3™  •  •  e""     Equations  for  the  boundaries  of  the  market  area  of  P" 


Number  of 
Unknowns 

n 

n 

m 
2n 

N 


Sum:  4n  +  ni  +  N 


Now  for  the  opposing  tendency  (see  p.  8,  note  8)  .  Under 
the  following  three  assumptions  the  number  of  independent  enter- 
prises is  as  large  as  possible,  in  individual  industries  and  in  the 
economy  as  a  whole:  The  locations  must  he  so  numerous  that  the 
entire  space  is  occupied  (Condition  2)  .  Furthermore,  in  all  activities 
that  are  open  to  everyone  abnormal  profits  must  disappear  (Condi- 
tion 3) .   Thus,  in  production,  prices  must  correspond  on  the  whole 


g6  Part  One.     Location 

to  costs. ^'^'®   In  consumption,  so  far  as  comparison  is  possible  at  all, 
the  advantages  must  be  evenly  distributed. 

This  condition  would  be  fulfilled  when  the  individual  volun- 
tarily decided  not  to  exhaust  all  possibilities  of  profit.  Nevertheless, 
there  would  still  be  room  for  new  competitors  since  the  areas,  as 
they  developed  under  the  existing  conditions,  could  be  made  yet 
smaller  without  detriment  to  the  profitability  of  the  industries  or 
farms  already  established.  In  addition,  therefore,  the  areas  of 
supply^  production,  and  sales  must  be  as  small  as  possible  (Condi- 
tion 4) ,  for  only  then  has  the  number  of  enterprises  that  can  survive 
reached  its  maximum.  If  still  more  farmers  or  entrepreneurs  should 
now  push  in,  all  enterprises  would  become  unprofitable.  Inde- 
pendent self-employed  producers  always  tend  in  general  toward 
this  point,  for  behind  them  is  the  inexhaustible  reserve  army  of 
dependent  employees,  poised  and  ready  to  jump  into  any  breach.^"" 

7.  It  may  happen  as  an  exception  that  even  the  greatest  possible  number  of  pro- 
ducers will  still  leave  the  marginal  entrepreneur  a  profit  small  but  within  these  limits 
maximized:  for  example,  when  an  area  is  larger  than  necessary  for  five  entrepreneurs 
but  not  large  enough  for  six.  The  situation  is  similar  when,  on  the  one  hand,  a  place 
offers  conditions  so  favorable  for  production  that  no  external  competition  can  approach 
closely  enough  to  take  away  all  profit,  but,  on  the  other  hand,  a  competitor  who  has 
established  himself  in  a  place  is  unable  to  develop  because  his  market  is  too  small. 

8.  To  these,  of  course,  belong  three  sources  of  income  that  sometimes  flow  in  an 
abundant  stream.  The  entrepreneur's  wage  for  his  personal  efforts,  which  falls  with 
decrease  in  the  size  of  the  business  until  the  income  of  the  marginal  entrepreneur  is 
so  small  that  the  influx  of  entrepreneurs  ceases;  the  payment  of  interest  on  his  own 
capital;  rent  for  the  productive  contribution  of  the  land  that  happens  to  belong  to 
him,  which  is  limited  in  area,  situation,  and  quality   (in  place  of  contractual  rent)  . 

9.  This  gives  for  each  of  the  n  locations  an  equation  of  the  general  form  tt^  =  k">, 
or  like  equation  No.  3  in  Table  4.  A  geometric  explanation  will  be  helpful.  The 
market  area  that  can  be  supplied  from  a  location  depends  on  the  one  hand  on  the 
shape  of  the  demand  and  on  the  other  on  the  shape  of  costs  within  the  firm.  Both 
are  illustrated  in  Figure  16a;  the  total  demand,  D,  within  this  market  area  as  a  func- 
tion of  f.  o.  b.  price,  and  total  production  as  a  function  of  the  costs,  k.  The  curves 
intersect  at  S  where  costs  and  price  are  equal. 

10.  In  geometric  terms,  a  diminution  of  the  area  means  a  shifting  of  the  demand 
curve  toward  the  left.  The  limit  of  this  diminution  is  reached  when  the  demand 
curve  is  tangent  to  the  supply  curve.  In  Figure  16a,  D'  is  the  shifted  demand  curve 
and  B  the  point  of  tangency.  Equation  3  contains  the  first  algebraic  condition  for  the 
tangency  of  the  two  curves;  the  second  condition  is:    (ir^) '  =  (k">) ',  or  like  equation  4. 

11.  It  might  appear  at  first  sight  that  condition  1  is  contained  within  condition  4, 
since  the  market  area  can  be  as  small  as  possible  only  when  the  factory  is  so  situated 
in  it  that  the  profit  is  as  large  as  possible.  But  condition  4  relates  only  to  the  size 
of  the  area,  independently  of  whether  it's  shape  is  appropriate;  and  conversely, 
condition  1  relates  only  to  the  shape  of  the  area,  independently  of  its  size.  For  the 
location  of  all  other  firms,  and  thus  the  order  of  magnitude  of  the  market  area  of  the 
selected  firm,  is  assumed  to  be  given,  whereas  under  condition  4  the  distance  between 


General  Location  Patterns 


97 


For  consumers,  on  the  contrary,  the  space  necessary  for  continuance 
of  an  individual  enterprise  is  a  minimum  only  in  overpopulated 
regions. 

Table  4.    SYSTEM   OF   EQUATIONS   I 


Condition 

Pertinent  Equation 
Equation  which  fulfills  condition 

Number  of 
Equations 

Maxi- 
mum 
num- 
ber of  -^ 
Pro- 
ducers 

1.  Maximum  profit 
(so  far  as  2-4 
permit 
'2.  Total  area  used 

3.  No  unusual 
profits 

4.  Area  as  small  as 
possible 

.5.  Boundaries 

Indiff'erence  lines 

as^             as™ 

^-  =  o;       — --  =  o 

<                   < 
S  Gf  +  Gl'  -f  . .  G™  =  G 

<P'^  (Dq)    =  X™  (Dq) 
dTTq      _  akq 

dGl     aG^ 

2n 

m 
n 

n 

N 

Sum:  4n  +  m  +  N  1 

Finally,  Condition  5:  At  the  boundaries  of  economic  areas  it 
must  be  a  matter  of  indifference  to  which  of  two  neighboring  loca- 
tions they  belong.   They  are  indifference  lines.^^'^^ 


locations  is  variable.  Hence  for  a  given  shape  of  the  area,  condition  4  is  supposed  to 
maximize  the  number  of  producers;  condition  1,  on  the  contrary,  maximizes  the  profit 
of  a  given  number  of  producers.  For  example,  condition  1  ensures  that  once  a  definite 
number  of  producers  has  been  reached  the  shape  of  the  area  on  a  uniform  plain  will 
be  that  of  a  regular  hexagon;  whereas  condition  4  ensures  that  this  hexagon  shall  be 
as  small  as  possible.  Profits  would  disappear  also  if  rectangles  were  made  sufl&ciently 
small.  Nevertheless,  the  number  of  producers  would  be  maximized  only  for  rectangles, 
not  in  general.  It  is  therefore  required  in  addition  that  the  shape  of  the  area  which 
is  being  reduced  be  economically  the  best. 

12.  For  any  given  point  {x,y)  on  the  edge  of  the  industrial  market  area  (factory 
price  +  freight  rate  x  distance)  must  be  the  same  whether  one  buys  from  P"»  or  P™i. 
For  the  geometric  form  of  the  border  see  pp.  165  f. 

13.  Everything  can  be  obtained  from  these  five  equations:  size  and  limits  of  market 
areas,  the  situation  of  production  locations  within  them  and  within  the  entire  area, 
and  f.  o.  b.  prices.  The  equations  from  which  possible  exchange  rates  could  be  deter- 
mined (Condition:  equilibrium  in  the  balances  of  payments)  have  been  omitted  from 
the  system  in  the  interest  of  simplicity.  Thus  it  presupposes  equal  currencies,  not 
only  in  the  ordinary  sense  but  in  the  strict  sense  to  be  employed  on  subsequent  pages, 
which  excludes  also  the  creation  of  money  by  banks.  Otherwise  the  price  levels  of  the 
various  bank  districts  would  appear  as  unknowns  instead  of  the  exchange  rates,  which 
would  then  have  to  be  determined  in  such  a  way  that  the  balances  of  payment  would 
be  in  equilibrium.   We  shall  return  to  this  in  Part  III. 

The  system  of  equations  under  discussion  could  be  expanded  still  further.  It  might 
be  desired  to  find,  say,  which  source  of  supplies  is  used,  and  how  efficiently;  or  the 
prices  of  land  parcels  and  who  receives  them. 


98 


Part  One.     Location 


b.     THE    SEPARATION    OF    LOCATIONS 


The  preceding  five  basic  conditions  must  be  fulfilled  if  the 
spatial  order  of  the  economy  is  to  have  meaning  and  permanence, 
but  they  do  not  guarantee  that  the  best  locations  for  production 
and  consumption  will  coincide.  On  the  contrary,  these  general 
equations  of  location  show  that  they  may  be  separate."  The  best 
location  for  producers  is  not  necessarily  also  the  best  for  consumers. 

With  free  competition  the  best  location  for  industrial  production 
is  also  the  most  favorable  for  consumers  of  industrial  goods,  to  be 
sure,  and  if  centers  of  agricultural  production  could  be  regarded 
exactly  as  are  those  of  industrial  production,  all  would  necessarily 
be  in  complete  harmony.  But  this  cannot  be  done.  Unlike  a  city, 
a  village  is  not  the  center  of  a  market  area,  but  merely  part  of  a 
production  area.  Agricultural  production  cannot  be  concentrated 
as  industrial  can;  dispersion  and  small  size  of  its  ultimate  units  are 
of  the  essence.  Hence  the  fundamental  contradiction  remains:  The 
best  location  for  the  production  and  consumption  of  industrial  goods 

14.  The  location  of  any  given  town  in  its  role  as  production  center  may  me  repre- 
sented by  the  coordinates  (x,  y)  and  as  a  center  for  consumption  by  (^,  tj)  .  The  first 
system  of  equations  determines  x  and  y,  and  |  and  t]  can  be  determined  by  a  very 
similar  one  that  will  not  be  derived  here,  however,  in  order  not  to  linger  over  extra- 
economic  matters.  If  we  were  to  expect  that  x  :=  |  and  )>  =  17  the  system  would  be 
overdetermined.  Consequently  the  best  location  for  a  town  as  a  production  site 
differs  from  its  location  as  a  site  of  consumption.  Just  as  little  do  their  supply  and 
market  areas  coincide,  except  at  the  level  of  the  economics  of  a  self-sufficient  town 
where  otherwise  the  balance  of  payments  between  town  and  country  would  not  be  in 
equilibrium. 

Nevertheless,  the  two  locations  of  consumption  and  production  are  interconnected. 
If,  in  the  equation  for  D»»  the  relation  between  D  and  (x,  y)  is  supposed  to  be  deter- 
mined not  only  by  varying  freight  costs  from  P  to  consumers  but  also  by  production 
costs,  which  in  turn  depend  upon  the  situation  of  P  with  respect  to  its  sources  of 
supply,  that  is  to  say  other  towns  and  the  open  coiuitry,  the  best  locations  for  producer 
and  consumer  are  combined  from  the  standpoint  of  the  industrial  entrepreneur.  As 
long  as  an  approach  to  the  best  location  lowers  labor  costs  for  the  consumer  of  agri- 
cultural goods  more  than  it  raises  his  freight  costs,  there  will  be  more  demand  for 
his  products.  He  will  therefore  leave  the  location  that  would  be  best  for  production 
if  the  optimum  location  for  a  producer  as  consumer  were  left  out  of  account,  for  the 
latter  location. 

Something  similar  will  occur  in  the  case  of  a  town  that  is  a  center  of  consumption. 
It,  too,  will  approach  an  industrial  location.  Thus  we  obtain  two  new  best  locations 
for  towns  as  producers  of  industrial  and  consumers  of  agricultural  commodities,  in 
the  determination  of  each  of  which  the  other  location  was  taken  into  account.  Now 
the  two  locations  may  be  nearer  to  each  other,  but  still  they  do  not  coincide.  Some- 
thing similar  can  be  shown  for  farmers  as  producers  of  agricultural  and  consumers  of 
industrial  goods. 


General  Location  Patterns  99 

by  themselves  is  a  great  city,  whereas  the  best  one  for  the  production 
and  consumption  of  products  of  the  soil  alone  implies  an  even 
distribution.  This  is  confirmed  by  the  distribution  of  populations 
in  earlier  times  and  today.  Formerly,  when  the  consumption  of 
agricultural  commodities  outweighed  that  of  goods  produced  by 
artisans,  there  were  many  small  towns. ^^  Later,  when  food  made  up 
only  a  part  of  living  costs,  even  for  the  workingman,  there  was  a 
tendency  toward  concentration  in  large  cities.  Today,  thanks  to 
improvements  in  transportation,  the  complete  separation  of  loca- 
tions has  become  a  reality.  Farmers,  of  course,  find  it  difficult  to 
live  away  from  their  farms,^**  but  industrial  workers  are  often  faced 
with  the  question  whether  to  live  where  they  are  employed,  or 
whether  the  cost  of  commuting  will  be  balanced  by  the  lower  living 
costs  and  greater  intangible  advantages  of  the  country  such  as  light 
and  air.  That  it  frequently  is  regarded  as  so  balanced  is  shown  by 
many  workers  who  daily  pour  into  industrial  towns  from  the  country, 
no  less  than  by  the  rural  and  semi-rural  suburbs  of  the  large  cities.^^-^^ 

c.     CONCLUSION 

The  significant  thing  in  our  derivation  is  not  that  we  can  heave 
a  sigh  of  relief  at  having  as  many  equations  as  there  are  unknowns.^^ 
It  was  to  be  expected  that  among  locations,  as  elsewhere  in  the 
economy,  equilibrium  would  be  possible  under  certain  conditions, 
but  it  is  important  to  be  clear  about  these  conditions. ^°    For  the 

15.  At  that  time  agriculture  could  still  constitute  the  determining  basic  stratum. 

16.  Yet  sometimes  they  do.  Many  ranch  owners  in  Texas  pass  the  week  ends  in 
their  town  houses,  but  stay  on  their  ranches  during  the  week. 

17.  The  cheaper  becomes  the  automobile,  the  farther  beyond  the  real  suburbs  does 
the  commuting  area  extend.  Distances  over  forty  miles  are  not  unusual  in  the  United 
States.  According  to  a  Gallup  poll,  only  about  three  per  cent  of  American  workers  live 
in  the  immediate  neighborhood  of  their  places  of  employment,  whereas  45  per  cent 
commute  either  in  their  own  cars  or  in  car  pools. 

18.  Another  important  example  is  the  separation  between  places  of  employment 
and  vacation  resorts  or  places  for  retirement.  Many  persons  move  from  localities  of 
lower  wages  and  living  costs  to  those  where  both  are  higher,  but  where  the  absolute 
amount  of  possible  savings  is  also  higher,  in  order  to  spend  these  savings  later  in  their 
places  of  origin  and  thus  considerably  increase  their  real  value.  This  is  the  attitude, 
for  example,  of  many  who  emigrated  to  America.  Conversely,  regions  of  lower  wages 
and  prices  are  less  attractive  to  those  who  wish  to  spend  their  savings  later  in  more 
expensive  localities. 

19.  In  the  case  or  regional  boundaries  the  equations  themselves  rather  than  the 
single  variables  have  been  counted,  as  an  exception,  among  the  unknowns  (see  Table 
3,  point  5)  , 

20.  In  my  opinion,  systems  of  general  equations  of  equilibrium  like  this  one  have 
no  other  significance.    I   consider   it  Utopian   to  assume   that   they   can   be  gradually 


lOO  Part  One.    Location 

conditions  of  this,  as  of  other  economic  equilibria,  must  first  be 
validated,  or  at  least  respected,  by  the  legal  framework  or  by  eco- 
nomic policy.^^  They  are  the  basic  principles  of  all  governmental 
intervention  where  the  restoration  of  equilibrium  is  concerned;  and 
they  form  the  framework  within  which  measures  for  obtaining  other 
public  objectives  must  be  kept  if  the  entire  economy  is  not  to  be 
endangered  or  incessantly  regulated.  Next  in  importance,  after 
establishing  that  an  equilibrium  exists,  is  to  show  how  it  looks. 
The  derivation  of  the  equations  ^^  shows  likewise  which  levers  can 
be  easily  regulated  if  the  need  should  arise. 

As  a  matter  of  fact,  most  phenomena  fall  between  these  general 
economic  principles  of  location  theory  and  the  empirical  methods 
of  the  theory  of  the  individual  firm,  which  we  can  neither  compre- 
hend nor  control  by  general  principles  or  individual  calculations. 
If  only  we  had  a  method  that  combined  the  generality  of  equations 
with  the  clarity  of  geometrical  figures!  Such  a  combination  would 
inevitably  have  weaknesses,  of  course,  since  in  a  strict  sense  it  is 
impossible.  But  does  not  the  path  of  science  include  many  pre- 
carious emergency  bridges  over  which  we  have  all  been  willing  to 
pass  provided  they  would  help  us  forward  on  our  road?  And  so  I 
hope  that  the  theory  of  economic  regions  to  be  developed  in  the 
following  pages  will  turn  out  to  be  a  path  into  a  rich  but  almost 
unknown  country. 


improved,  and  employed  to  solve  practical  problems  more  precisely  than  with  our 
present  coarse  methods.  After  all,  the  physicist  does  not  derive  the  law  of  freely  falling 
bodies  from  a  universal  formula,  nor  the  physician  his  remedy  from  a  general  formula 
for  treatment.  Still,  see  the  gallant  attempt  of  W.  W.  Leontief,  "Interrelations  of 
Prices,  Output,  Savings,  and  Investment.  A  Study  in  Empirical  Application  of  the 
Economic  Theory  of  General  Interdependence,"  Revieiu  of  Economic  Statistics,  XXIX 
(1937)  ,  109  ff.,  and  later  publications;  and,  more  recently,  that  of  H.  Peter  in  Finanz- 
archiv  und  Archiv  fiir  matliematische  Wirtschaftsforscliung,  1941. 

21.  This  is  least  true  for  condition  1,  the  fulfillment  of  which  is  ensured  by  the 
individual's  self-interest. 

22.  These  are  the  independent  variables  that  affect  equilibrium  without  its  reacting 
upon  them:  in  our  case,  for  example,  the  size  of  an  area,  the  direction  of  demand,  the 
technique  of  production,  and  the  level  of  freight  costs. 


PART   TWO.     ECONOMIC   REGIONS^ 


1.  The  basic  ideas  for  the  following  discussion  have  already  been  developed  in  my 
probationary  lecture  of  1936  before  the  Faculty  of  Law  and  Political  Economy  at  the 
University  of  Bonn  ("  Wirtschaftsgebiete  als  Grundlage  des  internationalen  Ilandels  ") , 
and  also  in  my  paper  read  before  the  Econometric  Society  at  its  1937  meeting  in 
Atlantic  City  ("  The  Nature  of  Economic  Regions  ")  .  The  English  lecture  was  pub- 
lished in  the  Southern  Economic  Journal,  V    (1938)  ,  71  ff. 


THE  THEORY  of  international  trade  has  proceeded  until 
now  on  the  assumption  that  states  are  the  most  important,  if 
not  the  only,  economic  units.  It  was  argued,  for  example,  that  if 
Germany  had  to  pay  reparations  to  France  the  German  price  level 
would  have  to  fall  and  that  of  France  would  have  to  rise  in  order 
to  make  the  transfer  possible.  But  no  doubt  it  might  just  as  well 
have  been  said  that  the  price  level  between  10  and  20  degrees  East 
longitude  and  45  and  50  degrees  North  latitude  would  have  to  fall, 
and  that  between  the  Meridian  of  Greenwich  and  10  degrees  East 
longitude  and  40  and  50  degrees  North  latitude  would  have  to  rise. 
In  other  words,  it  is  highly  improbable  that  the  line  dividing  falling 
and  rising  prices  coincides  exactly  with  political  boundaries.  Even 
though  it  could  be  shown  statistically  that  the  German  price  index 
was  falling,  this  would  prove  neither  that  prices  had  fallen  every- 
where in  Germany  nor  that  they  had  fallen  only  in  Germany.^  For 
instance,  it  is  very  unlikely  that  the  coal  mines  in  the  then  Polish 
Upper-Silesia  would  have  been  able  to  maintain  their  prices  if 
German  mines  a  few  miles  away  had  had  to  lower  theirs.  The  fact 
that  Upper  Silesia  constituted  an  economic  unit  would  seem  to  be 
more  important  in  many  respects  than  the  fact  that  it  was  politically 
separated  from  Germany.  On  the  other  hand,  suppose  large  subsidy 
payments  to  flow  from  western  Germany  toward  the  east.  In  such 
a  case  the  economic  consequences  would  resemble  those  of  war 
indemnities  to  a  hair.  Prices  would  necessarily  fall  west  of  the  Elbe 
and  rise  east  of  it.  Two  economic  regions  would  arise  in  the  same 
country. 

Of  course  no  one  any  longer  thinks  of  denying  that  political 
boundaries  are  also  economic  boundaries.^  The  preceding  examples 
are  meant  to  show  only  that  there  are  economic  regions  within 
political  boundaries  and  others  again  that  extend  beyond  them. 

This  has  not  remained  unnoticed,  and  a  few  writers  on  inter- 
national trade,  Ohlin  above  all,  have  endeavored  to  take  it  into 
account.    Their  investigations  belong  therefore  in  the  small  group 

2.  It  is  probable,  rather,  that  price  changes,  which  according  to  the  old  theory 
affect  a  particular  country,  really  extend  only  to  parts  of  it,  but  extend  to  neighboring 
countries  as  well.  In  the  case  of  small  or  long  and  narrow  countries  like  Canada  and 
Chile  this  is  immediately  obvious,  but  it  holds  also  for  those  whose  shape  is  better 
rounded,  as  we  shall  see  later   (pp.  302  ff.) . 

3.  To  what  degree  they  are  so  will  become  still  clearer  in  the  course  of  our  inquiry. 
But  the  differences  lie  elsewhere,  and  are  more  important  than  the  old  cylinder-piston 
theory  of  the  price  level  assumed. 

log 


104  Part  Two.     Economic  Regions 

of  fundamental  inquiries  into  economic  regions,^  Actually  they 
altered  little  more  than  words;  they  began  to  speak  of  interregional, 
in  addition  to  international,  trade;  and  what  had  held  for  states 
now  held  also  for  regions.  But  the  structure  of  these  economic 
regions  was  not  examined.  To  give  but  one  example:  The  fallacious 
idea  of  a  general  price  level  was  merely  split  into  fallacious  ideas 
of  regional  price  levels.  Yet  even  cursory  examination  of  the  nature 
of  such  a  region  would  have  shown  that  the  price  surface  was  much 
more  like  a  hilly  country  than  a  calm  lake.  Certainly  all  that  is 
included  in  an  economic  region  must  have  something  or  other  in 
common.  But  it  would  be  premature,  though  it  is  a  mistake  that 
suggests  itself  in  consciously  logical  procedures,  to  conclude  from 
this  that  since  prices  are  the  central  phenomena  in  all  exchange 
processes,  the  best  definition  of  an  economic  region  would  be  a 
region  throughout  which  prices  are  approximately  the  same.  This 
definition  is  unsuitable,  however,  because  there  are  no  such  regions; 
and  even  if  there  were  they  would  be  without  significance  and  thus 
not  worth  our  attention.  In  order  not  to  fall  into  a  similar  error 
we  shall  proceed  in  the  opposite  direction  and  try  to  discover 
whether  and  how,  under  rational  assumptions,  an  economic  boun- 
dary can  be  expected  to  arise.  Instead  of  starting  from  a  precon- 
ceived idea  we  shall  look  first  for  actual  differences,  and  not  until 
then  for  their  logical  common  denominator. 

4.  These  inquiries  have  many  different  origins.  Writers  on  location  theory  have 
provided  a  few  of  them  (besides  Thiinen,  Launhardt  in  particular,  and  recently 
H.  Ritschl  in  his  theory  of  the  economic  regions  [Kreise^,  "  Reine  und  historische 
Dynamik  des  Standortes  der  Erzeugungszweige,"  Schmollers  Jahrbuch,  1927) .  The 
history  of  economics  has  contributed  others;  G.  von  Schmoller's  economic  stages- 
village,  town,  territorial,  and  national  economy,  "  Das  Merkantilsystem  in  seiner 
historischen  Bedeutung,"  Schmollers  Jahrbuch,  1884:  also  K.  Biicher's  home,  town,  and 
national  economy.  Die  Entstehung  der  Volkswirtschaft   (1st  ed.,  1893) . 

Among  the  works  on  economic  geography  that  of  W.  Christaller  is  especially  to  be 
recommended.  Die  zentralen  Orte  in  Silddeutschland  (Jena,  1933) ;  and  "  Raumtheorie 
vmd  Rauraordnung,"  Archiv  fiir  Wirtschaftsplanung,  I    (1941) . 

The  American  economists  N.  S.  B.  Gras  (for  example,  "  The  Rise  of  the  Metro- 
politan Community,"  in  The  Urban  Community  [Chicago,  1926],  edited  by  E.  W. 
Burgess) ,  and  R.  D.  McKenzie  (The  Metropolitan  Community  [1933]) ,  among  others, 
have  written  on  the  economics  of  large  cities.  Factual  inquiries  are  much  more 
numerous,  but  all  suffer  from  a  lack  of  the  theoretical  background.  Ohlin's  book  was 
mentioned  above  because  it  has  much  in  common  with  the  writer's  volume,  at  least 
in  the  goal  set  though  not  in  the  solution  (C.  Brinkmann  to  the  contrary,  in  Finanz- 
archiv,  1940,  pp.  210  ff.) .  It,  too,  endeavors  to  combine  the  theories  of  location, 
economic  regions,  and  international  trade.  Yet  in  many  respects,  including  its  concise 
presentation,  Alfred  Weber's  neglected  essay  on  this  subject  seems  to  me  more  successful 
("Die  Standortlehre  und  die  Handelspolitik,"  Archiv  fiir  Sozialwissenschaft,  XXXII 
[1911],  667-688. 


A.  Economic  Regions  under  Simple  Conditions 


Chapter  9.     The  Market  Area 


Among  all  the  factors  that  can  create  an  economic  region  we 
shall  select  the  economic.  We  shall  consider  market  areas  that  are 
not  the  result  of  any  kind  of  natural  or  political  inequalities  but 
arise  through  the  interplay  of  purely  economic  forces,  some  v/orking 
toward  concentration  and  other  toward  dispersion.  In  the  first  group 
are  the  advantages  of  specialization  and  of  large-scale  production; 
in  the  second,  those  of  shipping  costs  and  of  diversified  production.^ 

In  the  following  derivation  we  start  from  radical  assumptions 
in  order  that  no  spatial  differences  may  lie  concealed  in  what  we 
assume:  that  economic  raw  materials  are  evenly  and  adequately 
distributed  over  a  wide  plain.  Our  area  shall  be  homogeneous  in 
every  other  respect  as  well,  and  contain  nothing  but  self-sufficient 
farms  that  are  regularly  distributed.  How  can  this  starting  point 
lead  to  spatial  differences? 

Let  us  select  any  one  of  these  farms,  and  ascribe  to  its  owner 
the  wish  to  produce  manufactured  goods  over  and  above  his  own 
needs.  Will  he  be  able  to  sell  them?  The  savings  due  to  mass  pro- 
duction will  favor  his  enterprise,  whereas  transportation  costs  will 
hamper  it.  How  large  will  his  market  eventually  be?  Suppose  his 
neighbors  are  of  the  same  stamp  and  live  similarly,  so  that  the 
demand  curve  for  one  is  typical  of  all.  Let  d,  in  Figure  20,  be  such 
an  individual  demand  curve  for  beer.  If  OP  is  the  price  at  the 
brewery,  which  is  at  P,  those  living  at  P  will  buy  PQ  bottles  of  beer. 

1.  As  the  advantages  and  disadvantages  of  specialization  may  be  reckoned  among 
the  advantages  of  mass  production,  we  contrast  only  these  latter  with  shipping  costs. 


io6 


Part  Two.    Economic  Regions 


Farther  away  the  price  will  naturally  be  higher  by  the  amount  of 
the  freight,  and  the  demand  consequently  smaller.  Still  farther  away, 
at  F,  where  Freight  costs  amount  to  PF,  no  beer  at  all  can  be  sold. 
Thus  PF  will  be  the  extreme  sales  radius  ^  for  beer,  and  total  sales 
in  this  district  will  be  equal  to  the  volume  of  the  cone  that  would 
result  from  rotating  the  triangle  PQF  on  PQ  as  an  axis    (Fig.  21) . 


Quantity 


^Quantity 


Fig.  20-22.  Derivation  of  the  demand  cone  (Fig.  21)  and  the  market  area  from  the 
demand  curve  for  the  product  as  function  of  distance  (Fig.  20)  and  the  cost  curves 
(Fig.  22) 

Its  volume  must  still  be  multiplied  by  a  constant  that  is  given  by 
the  population  density.  The  result  is  the  total  demand,  D,  at  the 
brewery  price  OP. 


2.  Freight  costs  expressed  in  marks,  not  in  kilometers.    To  reduce  to  kilometers 
it  is  necessary  only  to  divide  the  value  for  PF  by  the  freight  rate  per  kilometer. 


The  Market  Area  107 

Expressed  algebraically, 

D=^bX^  f  f{p-\-t)XtXdt. 
0 
where  D  =  total  demand  as  a  function  of  f.  o.  b.  price  p; 

b  =  twice  the  population  of  a  square  in  which  it  costs  1  mark 

to  ship  1  unit  along  one  side; 
7r=3.14-  •  •; 
d  =  f(p  -\-t) ,  individual  demand  as  a  function  of  price  at 

the  place  of  consumption; 
p  =  price  at  the  brewery; 

t  =  shipping  costs  per  unit  from  brewery  to  consumer; 
R  =  greatest  possible  shipping  cost   {PF  in  Fig.  20) . 

The  derivation  is  simple.  The  volume  of  a  solid  of  revolution 
is  equal  to  the  area  of  the  generating  surface  times  the  path  of  its 
center  of  gravity.  Let  the  surface  PQF  in  Figure  20  have  the  area 
F,  and  let  the  ordinate  of  its  center  of  gravity  (for  P  as  the  origin) 
be  Jo.  The  center  of  gravity  therefore  revolves  along  the  path  27r);o, 
and  the  area  of  the  generating  surface  27r)?o  X  F,  or 

R 

2^/  f  (p  -\-  t)  X  t  X  dt. 

0 

(since  according  to  the  formula  for  the  center  of  gravity 

R 

yoF=f  f{p  +  t)XtXdt). 

0 

Taking  into  account,  finally,  that  the  population  density  is  -^  we 

obtain  the  formula  given  above  for  D  as  a  function  of  the  brewery 
price  p.^ 

Actually  the  brewery  price  is  not  yet  given,  however,  as  we  have 
assumed  thus  far,  but  depends  on  the  total  demand.  Thus  the 
volume  of  the  demand  cone  must  be  calculated  for  various  arbitrary 

3.  It  had  already  been  given,  as  I  discovered  in  the  meantime,  though  in  somewhat 
different  form,  by  W.  Launhardt  (Mathematische  Begrundung  der  Volkswirtschafts- 
lehre  [Leipzig,  1885],  p.  152)  as  well  as  by  E.  Schneider,  following  Launhardt  ("  Be- 
merkungen  zu  einer  Theorie  der  Raumwirtschaft,"  Econometrica,  1935,  pp.  79-105; 
E.  M.  Hoover  ("  Spatial  Price  Discrimination,"  The  Review  of  Economic  Studies,  June, 
1937,  pp.  182-191)  ;  and  in  a  wholly  general  form  by  G.  Tintner  ("  Die  Nachfrage  im 
Monopolgebiet,"  Zeitschrift  fiir  NationaWkonomie,  1935,  pp.  536-539) . 


io8  P<^^i  Two.    Economic  Regions 

brewery  prices.  The  result  can  be  drawn  as  a  new  curve,  A  in 
Figure  22,  which  gives  total  demand  as  a  function  of  brewery  price. 
In  the  same  system  of  coordinates  we  draw  also  a  so-called  planning 
curve  TT,  which  gives  the  smallest  average  cost  at  which  any  given 
amount  can  be  produced.*  Only  if  the  supply  curve  tt,  and  the 
demand  curve  A,  intersect  can  our  farmer  open  a  brewery.  If  they 
do  not,  beer  cannot  become  a  marketable  product,  because  shipping 
costs  are  too  high  or  the  advantages  of  large-scale  production  too 
small.  Every  farmer  will  then  have  to  brew  his  own  beer  as  best 
he  can.  If  the  curves  intersect  at  N,  MN  will  be  the  total  amount 
of  beer  that  our  farmer  can  sell.  The  longest  market  radius,  or 
shipping  distance,  for  beer  in  this  case  will  be  equal  to  the  radius 
of  the  base  of  the  demand  cone  with  a  volume  2MN  -f-  B,  or  simply 
to  MF.  And,  like  beer,  every  economic  commodity  has  its  own 
maximum  shipping  distance,  beyond  which  it  cannot  be  sold.'^*' 


4.  This  minimum  can  be  reached  only  by  a  plant  that  has  been  built  especially  for 
this  capacity.  Its  average  cost  curve  touches  the  planning  curve  once,  but  otherwise 
runs  to  the  right  of  it.  Consequently  the  low  point  of  the  average  cost  curve  for  an 
individual  plant  lies  to  the  right,  below  the  point  of  tangency  with  ir.  However,  a 
plant  does  not  produce  more  cheaply  than  any  smaller  or  larger  one  the  amount  that 
corresponds  to  its  minimum  average  cost  point,  but  only  the  amount  that  corresponds 
to  its  point  of  tangency.  This  point  represents  the  capacity  for  which  it  was  built. 
For  since  the  point  of  minimum  average  costs  already  lies  above  the  planning  curve, 
another  and  larger  plant  would  evidently  be  more  advantageous.  This  is  easily  seen 
from  the  average  cost  curve,  K'  in  Figure  22  for  the  capacity  M'N'.  The  planning 
curve  represents  geometrically  the  envelope  of  the  average  cost  curves  for  plants  of 
various  sizes.  See  E.  Schneider,  "  Statische  Kostengesetze,"  National0konomisk  Tids- 
skrift,  LXX  (1932)  ,  Fig.  9,  p.  423;  J.  Viner,  "  Cost  Curves  and  Supply  Curves,"  Zeit- 
schrift  fiir  Nationalokojiomie,  1930. 

5.  Weber  {Vher  den  Standort  der  Industrien,  Pt.  I  [Tubingen,  1909],  pp.  240  fE.  and 
particularly  p.  244;  translated  by  C.  J.  Friedrich  as  Alfred  Weber's  Theory  of  the 
Location  of  Industries  [University  of  Chicago  Press,  1928])  treats  this  problem  in 
essentially  the  same  way,  as  an  "  agglomeration  of  originally  evenly  distributed  small 
scale  producers."  The  difference  is,  first,  that  this  deduction  is  not  correct,  because 
it  regards  demand  as  independent  of  local  price.  Secondly,  his  (marginal)  method 
is  different,  and  less  suited  to  the  Chamberlin  process.  And  thirdly,  he  does  not 
employ  this  process.  A  further  difference  is  didactic  in  nature:  He  starts  with  an 
unequal  distribution  of  natural  resources  and  introduces  agglomeration  later,  whereas 
we  proceed  in  the  opposite  direction. 

6.  As  soon  as  there  are  several  marketable  goods  their  price  relationships  are 
different  at  different  points  and  so  are  their  receipt  relationships  as  soon  as  their 
production  sites  agglomerate,  and  thus  strictly  speaking  their  demand  curves  are 
different,  too.  So,  for  example,  the  demand  curve  for  beer  differs  for  those  near  the 
brewery  and  for  those  at  a  distance.  But  however  significant  this  may  be,  we  must 
neglect  it  for  the  moment.   See  p.  143,  note  10. 


Chapter  10.     The  Network  of  Markets 


a.     CONTINUOUS   DISTRIBUTION    OF    POPULATION 
§1.     Size   of   Region 

The  deduction  so  far  would  be  relevant  if  economic  regions  were 
circular  in  form.  But  they  are  not.  Even  if  our  district  were  full 
of  breweries  lying  so  closely  together  that  their  sales  areas  touched, 
one  or  another  farmer  would  still  be  tempted  to  start  a  brewery 
for  himself.  And  he  could  do  so.  First,  because  all  the  corners 
between  the  circles  would  not  yet  have  been  fully  turned  to  account; 
and  second,  because  the  size  of  the  individual  brewery  could  be 
reduced  from  MN,  in  Figure  22,  to  M'N'  without  making  the  plant 
unprofitable.^ 

The  corners  can  be  utilized  by  pressing  the  circles  together  until 
a  honeycomb  results.  As  a  consequence  of  this  diminution  in 
regional  size  the  total  demand  curve  A  will  be  shifted  downward.^ 

1.  This  procedure  has  become  familiar  for  product  differentiation  through  the  work 
of  E.  H.  Chamberlin  {The  Theory  of  Monopolistic  Competition  [Cambridge,  Mass., 
1933;  5th  ed.,  1938])  and  of  Joan  Robinson  {The  Economics  of  Imperfect  Competition 
[London,  1933])  ,  but  it  holds  just  as  well  for  differences  in  location.  For  those  un- 
familiar with  the  literature  on  the  subject,  Chamberlin's  fundamental  ideas  will  be 
briefly  sketched:  (1)  With  product  differentiation  (which  here  includes  differences  in  the 
location  of  the  seller)  the  demand  curve  for  the  individual  seller  is  not  horizontal, 
as  with  homogeenous  products,  but  slopes  downward.  If,  for  instance,  a  seller  raises 
his  price,  not  all  his  customers  will  desert  him.  To  some  of  them  his  product  will 
offer  advantages,  such  as  convenience  of  location,  that  are  worth  even  the  higher  price. 
(2)  As  long  as  the  demand  curve  intersects  the  cost  curve,  surplus  profits  that  attract 
competitors  are  possible.  These  will  turn  out  differentiated  products  or,  which  is  of 
special  interest  in  the  present  context,  will  choose  the  location  of  their  establishments 
in  such  a  way  that  they  are  particularly  convenient  for  some  of  the  buyers.  As  a 
consequence  of  this  loss  of  purchasers,  the  demand  curves  of  the  earlier  enterprises 
will  shift  to  the  left  until  they  are  tangent  to  the  cost  curve  and  all  surplus  profits 
disappear.  The  tendency  to  the  maximization  of  independent  enterprises  that  underlies 
the  process  just  described  now  reaches  its  limits.  Small  surplus  profits  may  still  remain, 
however,  if  an  area  is  larger  than  necessary  for  n  producers,  but  not  large  enough  for 
n  +  L  If  n  =  1,  there  is  a  monopoly  which,  of  course,  is  restricted  by  latent  com- 
petition that  may  become  actual  if  the  monopoly  is  exploited  to  the  full.  Then  comes 
a  struggle  between  the  earlier  and  the  later  firms,  one  of  which  must  finally  succumb 
since  there  is  not  room  for  both. 

2.  With  increasing  curtailment  in  the  size  of  a  region,  the  point  of  rotation,  G, 

109 


,  10  Part  Two.    Economic  Regions 

But  the  hexagon  can  be  made  even  smaller,  until  the  total  demand 
curve  A'  still  just  touches  the  supply  curve  tt.  Then  the  market  is 
full.  If  still  another  brewery  were  to  be  established,  the  market 
area  would  not  be  large  enough  for  all,  and  the  two  curves  would 
no  longer  be  even  tangent.  If  the  longest  possible  sales  radius  R 
corresponds  to  the  total  sales  MN,  the  shortest  possible  radius  p  ^ 
would  correspond  with  the  total  sales  MW;  p  also  is  characteristically 
different  for  different  goods.*  Figure  23  shows  the  transition  for 
the  same  commodity  from  the  largest  to  the  smallest  possible  sales 
area.^ 


Fig.  23.    Development  of  market  areas  from  the  large  circle  to  the  final  small  hexagon 

§2.     Shape   of   Region 

Geometrically  speaking  there  are  two  other  possibilities  for 
utilizing  the  corners  between  market  circles:  triangular  or  square 
economic  regions  can  be  imagined.  But  the  hexagon  has  the  advan- 
tage of  being  nearest  to  the  ideal  circular  form.  Consequently 
among  all  three  possibilities  the  demand  per  unit  of  area  is  greatest 
with  the  hexagon. 


moves  upward  on  A.  It  is  determined  by  FE,  which  is  equal  to  the  radius  of  the 
region  at  the  time,  expressed  as  freight  costs.  V,  the  lower  end-point  of  the  shifted 
demand  curve.  A',  is  determined  by  the  fact  that  OV  must  equal  the  volume  of  a  cone 
developed  by  rotating  the  surface  OABT  about  OT  as  an  axis.  OA  again  is  equal  to 
the  radius  of  the  region. 

3.  p  represents  the  radius  of  the  inscribed  circle. 

4.  This  we  know  from  daily  experience.  Suppose  one  is  to  have  a  cake  baked  near 
home.  Nobody  would  carry  the  heavy  pan  of  batter  across  the  whole  town,  even  to 
the  best  baker.  Bwfno  one  would  mind  a  long  trip  to  leave  a  watch  for  repair  with 
a  skillful  watchmaker,  and  one  would  go  even  outside  the  town  to  a  medical  specialist. 

5.  Diminution  of  a  region  is  disadvantageous  for  the  established  entrepreneur, 
because  his  profits  disappear;  it  is  welcome  to  the  newcomer  because  then  there  are 
more  possibilities  of  making  himself  independent;  and  it  is  often  advantageous  for  the 
consumer  because  although  the  price  at  the  plant  usually  rises,  the  average  freight 
costs  fall. 


Network  of  Markets 


Table  5.   DEMAND   AS   A   FUNCTION   OF   REGIONAL   SHAPE 


Size  of  Demand  1                                              j 

Shape  of 
Market  Region 

Total 

Per  unit  of 

area 

of 

entire  region 

of 
region  utilized 

Large  circle^ 

R2H  1.047204) 

0.302  H 

0.333  H 

Small  circle^ 

of 
equal 
area 

r2H  (2.598 -J^l.575) 

0.907  H -0.550  H^3) 

H- 0.606  H^4) 

Hexagon 

r2H  (2.598-^1.580) 

H -0.608  H^O 

H -0.608  H^ 

Square 

r2H  (2.598-' 1.602) 

K 

H-0.617  H^ 

H-0.617  H^ 

Triangle 

r2H  (2.598-^1.690) 

H-0.651  H| 

H-0.651  H^ 

1.  R  =  radius  of  base  of  original  cone.     (Largest  possible  shipping  costs,   PF  in 

Fig.  20.) 
r  =  radius  of  the  circle  circumscribed  about  the  hexagonal  area  of  base  removed 
(r<R). 
H  =  height   of  demand   cone.     (Individual   demand   at   site   of   factory,   PQ   in 
Fig.  20.   For  the  sake  of  simplicity  it  is  assumed  that  the  population  density 
b/2  is  1.) 

2.  Large  circle,  radius  R;  small  circle,  radius  G.909r. 

3.  It  is  easily  seen   that   this  quantity  is  smaller  than   that  corresponding  to  the 
hexagon  if  r  is  given  the  limiting  values  of  O  and  R. 

4.  The  highest  value  in  the  column  concerned. 

For  the  case  of  a  linear  demand  curve  *  a  more  rigorous  proof 
can  be  adduced.  Let  the  ruling  QF  of  the  cone  in  Figure  21  be  a 
straight  line,  and  let  the  height  P(l  be  equal  to  H  and  the  radius 
of  the  base  PF  be  equal  to  R.   If  the  cone  is  cut  by  a  plane  parallel 


6.  This  will  be  assumed  more  frequently,  for  it  is  not  only  an  especially  convenient 
assumption  but  an  especially  reasonable  one.  If  OF,  as  in  Figure  20,  is  the  price  at 
which  nothing  more  will  be  sold,  and  OT  the  amounts  that  would  be  consumed  if 
the  good  were  free,  then  OF  and  a  line  parallel  to  it  through  T,  and  OT  and  a  parallel 
line  to  it  through  F,  will  in  almost  all  cases  delimit  the  area  in  which  the  demand 
curve  must  lie.  We  now  choose  our  scale  in  such  a  way  that  OF  is  equal  to  OT,  so  that 
these  lines  and  their  two  parallels  form  a  square.  If  we  draw  in  this  square  all  con- 
ceivable forms  of  demand  curves  and  the  diagonal  FT,  the  resulting  triangles  and  all 
portions  of  the  possible  demand  curves  lying  within  them  will  be  congruent  and 
symmetrical  in  resepct  to  FT.  The  sum  of  the  deviations  from  FT  is  zero.  The  straight 
line  FT  is  the  average  value  of  every  possible  form  of  demand  curve.  In  all  cases 
where  no  details  are  known  about  the  actual  shape  of  the  demand,  the  linear  form  is 
the  only  well-founded  assumption. 


Part  Two.     Economic  Reaions 


to  the  axis  of  rotation  at  the  distance  p,  the  volume  ^  of  the  portion 
of  cone  cut  off  will  be 


^=  f  (i?^  arc  cos  ^- 2pV^^^  +  2.302632  |- log  ^+^^^^^^ 

We  now  cut  the  demand  cone  through  planes  parallel  to  the  axis 
in  such  a  way  that  an  equilateral  triangle,  a  square,  or  a  hexagon  of 
equal  area  appears  as  a  base.  The  volumes  of  the  portions  of  cone 
remaining  above  are  then  proportional  to  the  total  demand  for  the 
market  areas  concerned.  These  volumes  are  calculated  by  the 
formula  given  above,  and  Table  5  shows  the  result.  For  comparison 
the  cone  is  cut  also  by  a  vertical  cylinder  the  base  of  which  has 
the  same  area  as  the  figures  just  edscribed. 

The  result  is  that  the  demand  of  the  market  area  as  a  whole  is 
greatest  when  this  area  is  not  curtailed  at  all.  The  demand  of  the 
curtailed  sales  area  is  greatest  when  it  is  circular  in  form.  But  per 
unit  of  area  of  the  market  region,  the  demand  of  the  small  circle, 
not  that  of  the  large  circle,  is  greatest  because  in  the  latter  case  the 
average  for  the  area  is  reduced  by  the  small  demand  near  the  limits 
for  shipment.  The  average  demand  in  the  small  circle  is  obviously 
greater  than  in  any  polygon  of  equal  area.  But  because  circles 
leave  empty  corners,  the  demand  per  unit  of  the  entire  area  in  the 
case  of  the  hexagon  exceeds  not  only  that  of  a  square  and  a  triangle, 
but  even  that  of  a  circle.  In  other  words,  among  all  the  possi- 
bilities of  realizing  the  same  total  demand,  the  most  land  is  required 
with  a  triangle,  and  the  least  with  a  regular  hexagon.  The  honey- 
comb is  therefore  the  most  advantageous  shape  for  economic  regions.^ 
The  advantage   benefits  consumers  as   a   whole, ^   whereas   for  the 

7.  Professor  C.  H.  Sisam,  of  Colorado  Springs,  was  so  kind  as  to  derive  this  formula 
for  me.   Arc  cos  is  to  be  taken  as  an  arc,  not  as  an  angle. 

8.  The  regular  hexagon  is  the  most  advantageous  shape  for  a  market  area  just  as 
it  is  for  the  true  honeycomb,  but  for  not  quite  the  same  reasons.  With  the  true 
honeycomb  the  ratio  of  perimeter  to  area  must  be  especially  favorable;  with  the 
market,  the  ratio  of  cone  to  area.  In  both  cases  the  circular  form  would  be  best  were 
it  not  for  the  empty  corners.  The  result  of  these  is  that  in  one  case  the  wax,  in  the 
other  the  demand,  is  not  utilized  to  the  full.  Among  all  the  possibilities  of  utilizing 
the  corners,  the  hexagon  retains  most  of  the  advantages  of  the  circle.  The  size  of  the 
hexagon  depends,  of  course,  upon  totally  different  factors. 

9.  So  far  we  have  proved  only  that  the  hexagon  is  superior  to  other  regional  shapes; 
nothing  has  been  said  about  the  best  size  of  the  hexagon.  It  remains  an  open  question 
whether  the  Chamberlin  process  (incomplete  utilization  of  the  capacity  of  a  region 
with  a  concomitant  rise  in  price  because  of  an  increased  number  of  competitors)  is  of 
advantage  to  consumers.  In  the  proof  given  above,  the  producer's  price  could  be 
regarded  as  practically  constant  in  so  far  as  the  market  areas  differ  only  in  form,  not 


Network  of  Markets  113 

individual  producer  the  uncurtailed  large  circle  would  be  most 
favorable.  But  because  free  competition  results  in  the  elimination 
of  undeserved  profits,  it  is  a  matter  of  indifference  to  the  entrepre- 
neur how  his  region  is  cut  down.  Yet  the  honeycomb  shape  con- 
tributes to  the  advantage  of  producers  as  a  whole  also,  since  it  makes 
possible  the  largest  number  of  independent  enterprises. 

It  is  easy  to  see  from  the  table  how  great  is  the  advantage  of 
the  hexagon.  As  compared  with  the  other  polygons,  the  advantage 
varies  with  r;  it  is  greatest  when  r  =  R,  where  as  it  disappears 
entirely  for  r  ^  0.  As  compared  with  the  small  circle,  it  is  almost 
independent  of  r.  In  the  maximum  case  the  demand  in  a  hexagon 
is  2.4  per  cent  greater  than  in  a  square  of  equal  size;  always  about 
10  per  cent  greater  than  in  a  circle,  if  the  empty  corners  are 
included;  and  at  a  maximum  12  per  cent  greater  than  in  an  equi- 
lateral triangle  of  the  same  area.  The  superiority  of  the  hexagon 
over  the  square  is  least,  and  of  no  practical  importance  in  many 
instances,  its  advantage  being  greatest  in  comparison  with  the 
triangle  and  the  circle— at  least  when  the  individual  demand  curve 
is  a  straight  line. 

For  curves  of  other  form  the  advantage  of  the  hexagon  may  be 
greater  or  less,  but  it  changes  to  a  disadvantage  only  in  a  few  of 
those  unusual  cases  in  which  demand  increases  with  rising  price. 
Compared  with  a  linear  demand,  the  advantage  of  the  hexagon 
becomes  greater,  the  more  elastic  the  demand  at  the  boundaries  of 
the  region,  and  smaller  the  more  inelastic  is  this  demand."   In  the 


in  size.  In  judging  the  reduction  of  sales  areas  it  is  important  to  know,  however, 
whether  the  average  saving  in  freight  will  be  greater  than  the  increase  in  costs  of 
production;  that  is,  whether  b,  in  Figs.  20,  22,  and  41,  will  be  exceeded  by  a.  This 
need  not  always  be  the  case.  An  entirely  similar  problem  is  posed  in  governmental 
organization.  Not  every  simplifying  of  administration  makes  matters  easier  for  the 
governed  as  well.  If  it  is  proposed,  for  example,  to  merge  small  administrative  districts 
into  larger  ones,  any  possible  economies  in  government  must  be  weighed  against 
traveling  expenses  for  the  citizens. 

It  is  a  somewhat  different  question  whether  these  differences  in  expenditure  are 
large  enough  to  be  statistically  shown;  that  is  to  say,  whether  it  can  be  decided  from 
differences  in  nominal  costs  of  the  order  of  magnitude  here  considered,  in  which  case 
the  real  costs  will  be  greater.  An  analogous  situation  will  be  discussed  in  more  detail 
below  on  pp.  327  f.  in  connection  with  free  trade,  and  on  pp.  490  ff.  in  connection 
with  the  cost  of  living.  See  also  H.  Schmidt,  Die  wirtschaftliche  Mengenteilung  des 
nationalen  Bedarfes  eines  Erzeugnisses    (Berlin,  1942)  . 

10.  In  comparing  the  hexagon  with  the  square,  for  instance,  the  boundary  region 
is  to  be  reckoned  from  the  inscribed  circle  of  the  hexagon  to  the  circumscribed  circle 
of  the  square.  The  elasticity  within  the  inscribed  circle  is  less  important  for  the  com- 
parison, and  the  elasticity  outside  the  circumscribed  circle  is  of  no  consequence  at  all. 


11^  Part  Two.    Economic  Regions 

first  case,  for  example,  the  demand  will  fall  rapidly  with  the  distance 
from  the  production  site,  a  fall  that  becomes  increasingly  greater  as 
larger  portions  of  the  market  area  such  as  the  corners  of  triangles 
lie  relatively  far  from  the  center. 

The  size  and  shape  of  the  entire  region  also  exert  an  influence 
on  the  favorability  of  the  honeycomb  shape.  Thus  if  the  whole 
region  is  small  in  relation  to  the  area  of  the  individual  market,  or 
very  irregular,  wide  departures  from  the  shape  that  imply  an 
enlargement  of  the  region  may  become  necessary  if  the  whole  region 
is  to  be  fully  utilized. 

In  summing  up  it  may  be  said  that  the  regular  hexagon  becomes 
more  favorable  as  a  regional  shape  the  larger  and  more  rounded-off 
the  whole  area,  the  more  elastic  the  demand  at  the  boundaries,  and 
the  more  closely  the  necessary  shipping  distance  approaches  the 
possible  one.^^ 

b.     DISCONTINUOUS    DISTRIBUTION    OF    POPULATION 

For  every  commodity  the  proposition  holds  good,  that  a  market 
area  with  the  form  of  a  regular  hexagon  and  an  inscribed  circle  of 
radius  p  that  is  specific  for  this  commodity,  is  necessary  and  sufficient 
to  make  its  production  possible.  On  the  one  hand,  p  depends  upon 
the  cost  curve,  which  for  the  time  being  is  assumed  to  be  given; 
and  on  the  other  hand,  upon  the  demand.  This,  rgain,  can  be 
traced  back  to  two  factors:  The  individual  demand  curve,  whose 
influence  we  have  so  far  been  examining;  and  the  consumers,  whom 
we  have  for  the  sake  of  simplicity  assumed  to  be  equally  and  con- 
tinuously distributed  over  our  area.  If  this  were  so,  p  could  have 
any  value.  But  in  reality  the  number  of  possible  values  of  p  is 
limited,  because  the  population  may  be  equally  but  not  continu- 
ously distributed.   Whatever  the  smallest  settlements  may  be— single 

11.  I  have  found  the  hexagonal  shape  discussed  in  two  places  in  the  literature, 
though  without  adequate  proof.  First,  by  W.  Launhardt  (Mathematische  Begriindung 
der  Volkswirtschaftslehre  [Leipzig,  1885],  p.  181) ,  who  assumed  it  only  by  way  of 
example;  and  recently  in  the  admirable  book  by  W.  Christaller  (Die  zentralen  Orte  in 
Siiddeutschland  [Jena,  1933]) ,  who  at  least  advanced  a  general  though  inadequate 
proof.  According  to  Christaller  the  hexagonal  arrangement  of  central  sites  has  the 
advantage  "  that  they  are  neither  too  few  nor  too  many,  and  also  that  no  districts  are 
left  without  regular  supply"  [ibid.,  p.  69)  .  H.  Haufe  {Die  geographische  Struktur  des 
deutschen  Eisenbahnverkehrs  [Langensalza,  1931],  pp.  14  f.)  finds  hexagonal  networks 
of  transport  lines  most  favorable  for  the  uniform  spherical  surface  of  the  earth  because 
with  them,  though  not  of  course  with  the  triangles  into  which  they  necessarily  divide, 
the  relation  of  these  lines  to  the  regions  they  serve  is  advantageous;  and  because 
hexagons,  like  triangles  but  unlike  squares,  can  cover  the  earth  without  a  remainder. 


Network  of  Markets  1^5 

farms,  hamlets,  or  villages  ^^—they  are  separated  from  one  another 
by  certain  distances  that  may  be  neglected  only  when  they  are  small 
in  relation  to  the  market  area.  With  most  commodities,  however, 
the  situation  and  size  of  the  original  settlements  exerts  a  considerable 
influence  on  the  situation  and  size  of  the  market  area.  This  influence 
we  shall  now  proceed  to  examine. 

Let  a  be  the  distance  between  the  smallest  settlements  Ai,  A  2, 
and  so  on,  which  we  have  assumed  to  be  farms.  Again  the  most 
suitable  shape  of  their  area  is  that  of  the  regular  hexagon.  Conse- 
quently their  centers,  where  the  buildings  are  set,  lie  at  distances 
of  a  kilometers  on  straight  lines  that  cross  at  an  angle  of  60°  or 
120°,  not  at  right  angles  as  on  a  square  farm— a  distribution  that 
may  be  described  as  honeycomb  scattering.^^ 

12.  For  farmers  as  producers  the  advantages,  for  farmers  as  consumers  the  disadvan- 
tages, of  scattered  settlements  may  preponderate.  Scattering  shortens  the  distance  from 
farm  buildings  to  fields  except  with  mixed  cropping,  but  lengthens  the  distance  from 
the  center  of  the  village  and  generally,  also,  from  the  town  to  the  farm  buildings  or 
its  fields.  This  affects  the  farmer  in  uncultivated  country,  not  only  as  pure  consumer 
but  also  as  producer,  in  so  far  as  he  employs  such  outside  aids  to  production  as  the 
help  of  neighbors,  co-operatively  owned  machines,  water  power,  electricity,  coal,  or 
artificial  fertilizers,  and  in  so  far  as  he  sells  his  produce.  This  variation  in  distance, 
the  net  effect  of  which  depends  upon  circumstances,  becomes  more  important:  (1)  the 
greater  it  is,  as  in  the  case  of  districts  that  are  especially  large  because  of  limited  or 
sporadic  productivity  in  regions  that  are  mountainous,  wooded,  or  rich  in  lakes;  or 
because  wide  areas  are  used,  as  on  ranches  in  Texas;  (2)  the  heavier  the  road  traffic  is, 
whether  because  of  the  size  of  loads,  for  example,  with  extensive  fertilization  or 
naturally  high  yields,  or  because  the  number  of  trips  is  larger  (as  with  cattle,  schools, 
churches,  government  offices,  daily  requirements— in  so  far  as  these  cannot  be  cheaply 
produced  in  small  quantities,  as  with  goods  needing  a  large  market  area;  (3)  the 
higher  the  costs  per  mile  and  the  more  they  differ  for  villages  as  against  more  dispersed 
settlements.  These  differences,  which  were  formerly  more  important  than  they  are 
today,  favored  a  scattering  of  the  population  if  distances  could  be  shortened  at  all 
thereby;  and  without  question  they  are  higher  in  areas  whose  settlements  are  widely 
scattered  because  roads  are  worse  or  more  expensive  and  transportation  on  a  small  scale 
more  costly  despite  the  motor  truck. 

Thus  the  type  of  settlement  that  is  economically  most  advantageous  varies  with 
circumstances;  only  the  intermediate  form,  a  sprawling  village,  generally  combines  the 
disadvantages  of  both  kinds.  Nor  are  the  effects  of  recent  developments  by  any  means 
unequivocal;  inventions  like  the  telephone  and  the  radio  encourage  scattered  settle- 
ments, whereas  the  increasing  interlacing  of  markets  favors  the  establishment  of  villages. 
The  issue  is  often  decided  by  extra-economic  considerations.  In  scattered  settlements 
the  greater  vulnerability  to  attack  by  nature  and  by  man  must  be  taken  into  account, 
but  above  all  the  high  price  that  is  paid  for  greater  freedom.  Isolation  does  not  suit 
most  people  and  seclusion  may  easily  destroy  community  life,  for  culture  flourishes 
better  in  the  stimulating  life  of  not  too  large  towns.  See  p.  28,  note  31,  and  W. 
Christaller,  Die  Idndliche  Siedhingsweise  im  deutschen  Reich    (Stuttgart,  1937) . 

13.  In  Latin  it  is  called  quincunx,  and  in  English  lattice.    The  distribution  is  that 


ii5  Part  Two.    Economic  Regions 

Let  b  be  the  distance  between  the  small  market  towns  ^i,  B2, 
and  so  on,  as  we  shall  call  the  smallest  places  where  industrial  goods 
are  produced  for  sale,  b  corresponds  to  the  diameter  of  the  inscribed 
circle  2p  of  the  market  area,  except  that  p  is  expressed  in  freight 
costs  and  b  in  kilometers  or  miles. 

Let  nV  he  the  necessary  shipping  distance;  that  is,  the  greatest 
distance  at  which  a  commodity  must  be  sold  to  make  its  production 
worth  while.  But  this  does  not  mean  that  all  farms  lying  within 
this  circumference  will  be  supplied  by  the  market  town  concerned, 
except  where  nV  equals  the  radius  of  the  inscribed  circle.  Nor  can 
wF  be  simply  identified  with  the  radius  r  of  the  circumscribed  circle 
of  the  hexagon,  for  often  there  are  no  settlements  at  all  along  the 
boundary,  or  at  least  in  its  corners.  Thus  with  a  discontinuous 
population,  n  F  is  independent  of  r  and  of  p  or  b/2,  respectively. 

§1.     Relative   Positions   of   Settlements 

We  shall  now  examine  the  ten  smallest  market  areas  with  respect 
to  size  and  location.  The  smallest  possible  value  for  the  necessary 
shipping  distance  is  obviously  the  distance  between  the  farms  as 
long  as  we  assume  that  production  takes  place  on  one  of  these,  A-^ 
(settlement  site) ,  and  not  in  a  building  erected  between  them  for 
this  purpose.  The  smallest  possible  value  for  the  number  of  settle- 
ments supplied,  however,  including  A^  itself,  is  not  7,  but  3.  For 
it  is  conceivable  that  there  is  a  product  for  which  A^,  which  develops 
into  a  market  town  B^,  does  not  need  the  entire  demand  of  the 
6  neighboring  farms  in  order  to  recover  its  costs.  It  might  share 
instead  with  the  neighboring  market  towns  B2  and  B3  in  supplying 
the  needs  of  farm  A  2,  and  similarly  supply  only  one  third  of  the 
needs  of  each  of  the  farms  A^  to  A-,  (Fig.  24) .  When  these  shares 
are  added,  market  area  1  contains  [the  equivalent  of]  three  fully 
supplied  settlements.  Its  areau  F,  is  a^-Sy/S-^2,  and  the  distance 
between  market  towns  is  ay/ 3. 

For  the  next  larger,  area  2,  nV  is  still  equal  to  a,  but  now  the 
demands  of  neighboring  farms  are  so  shared  among  adjacent  com- 
petitors that  Bi  receives  the  entire  demand  of  three  neighboring 
farms,  which  together  with  its  own  makes  four  (Fig.  25).  From  this 
it  follows  that  area  2  must  be  oriented  differently  from  area  1.  Its 
borders  are  not  simply  parallel  to  those  of  the  latter.  Consequently 
b  also  is  now  larger,  namely  «V4,  though  nF  is  still  equal  to  a. 


of  the  crossing-points  of  strips  in  a  fence  where  one  series  is  inclined  to  the  left  at  an 
angle  of  60°  and  the  other  is  nailed  over  it  at  a  similar  angle  toward  the  right. 


Network  of  Markets 


117 


There  remains  yet  a  third  area  for  which  nF  is  equal  to  a,, 
though  it  is  the  sole  supplier  of  seven  farms.    Area  3  offers  an 
example  of  a  boundary  line  that  runs  through  open  fields  without 


•       .       •       • 

X 

.-^      .^ 

X 

'^\/-^-\. 

Figs.  24-26.    The  three  smallest  market  areas 

touching  any  settlement  (Fig.  26) .  Though  such  a  boundary  has, 
therefore,  no  immediate  economic  significance,  the  survey  is  facili- 
tated if  we  know  how  it  runs.  This  border,  again,  is  not  parallel 
to  the  boundaries  of  the  first  two  areas. 

The  three  smallest  market  areas  show  three  typical  orientations 
at  the  same  time  (Fig.  27) .  Assuming  that  one  of  the  straight  lines 
on  which  the  farms  follow  each  other  at  distance  a,  is  horizontal 
in  the  figure,  the  first  orientation  is  such  that  the  hexagon  rests  on 
one  side  (e.  g.,  areas  1  and  5) .  In  the  second  orientation  it  stands 
on  one  corner  (e.  g.,  areas  2,  4,  7,  and  10) ) .  In  the  third,  it  is 
inclined  to  a  varying  degree   (e.  g.,  areas  3,  6,  8,  and  9) . 

Table  6  contains  the  most  important  measurements  for  to  10 
smallest  possible  market  areas.  From  it  is  derived  an  extremely 
simple  relation  between  n,  the  number  of  settlements  supplied,  and 
b,  the  distance  between  the  market  towns  that  supply  them.    It  is 

b  =  a^/H 


ii8 


Part  Two.     Economic  Regions 


Expressed  in  words:  The  distance  between  tiuo  enterprises  of  the 
same  kind  is  equal  to  the  distance  between  the  settlements  supplied 
times  the  square  root  of  their  number.  Furthermore,  the  number 
of  whole  settlements  included  within  a  market  area  increases 
according  to  a  definite  law,  as  can  be  seen  from  Table  7."'  Finally, 
the  size  of  a  market  area  can  be  very  simply  calculated.  It  is  always 
equal  to  a"nV3-f-2. 


^•' 


l\    iV,     1^     1^ 
1    +^     ^1 


10 


■^■^^J^ 


■/;■/■'} 


Fig.  27.  The  10  smallest  economic  areas.  The  sectors  containing  many  towns 
are  hatched.  Alternative  regional  centers  are  in  parentheses.  Simple  points 
represent  original  settlements.  Those  enclosed  in  circles  are  centers  of  market 
areas  of  sizes  indicated  by  the  figures. 


13a.  August  Losch  did  not  give  the  actual  formula  for  this  law  by  means  of  which 
n  could  be  calculated  for  any  desired  market  area.  From  inspection  of  Table  7, 
Professor  Werner  Kanzig  of  the  Department  of  Physics,  University  of  Illinois,  has 
kindly  supplied  the  following  general  method  of  finding  the  number  of  settlements 
corresponding  to  the  /jth  area.  The  general  formula  used  by  Losch  has  the  form 
(feV3)  -  +  Z-  =r  r?,  where  n  is  the  number  of  settlements.    Let  the  number  of  the  area. 


Network  of  Markets  »i9 

Table  6.   THE   TEN   SMALLEST   POSSIBLE   MARKET   AREAS 


11  =  number  of  settlements  completely  sup- 
plied, including  the  point  of  supply. 
Those  partly  supplied  are  reckoned  in 
terms  of  the  equivalent  number  of 
fully  supplied  settlements. 

1)  =  distance  between  points  of  supply  c= 
distance  between  centers  of  areas  = 
diameter  of   inscribed   circle. 

nV  =  necessary  shipping  distance  =  distance 
of  seller  from  farthest  still  necessary 
customer. 


Area 

No. 

n 

b 

nV 

1 

3 

.f^ 

a 

2 

4 

a)/  4 

a 

3 

7 

al/7 

a 

4 

9 

aV, 

.f^ 

5 

12 

al/,2 

2a 

6 

13 

al/,3 

.f. 

7 

16 

a|/l6 

2a 

8 

19 

a|/l9 

2a 

9 

21 

a|/21 
a)/ 25 

.fy 

10 

25 

al/7 

a  =  distance  separating  original  settlements. 


Table   7.    CALCULATION    OF   n 


Area 
No. 

n 

Area 

No. 

n 

1 
2 
5 
6 
7 
11 

(1  .  1/3)2  +  02  =     3 

3 

(1>^  1/3)2+      (^)2    =      7 

(1  .1/3)2  +  12  =     4 
(2  .  1/3)2  +  02  =  12 
(2  .  1/3)2  +  12  =  13 
(2  .  1/3)2  +  22  =  16 
(3  .  1/3)2  +  02  =  27 

4 
8 

(1^^1/3)2  +  (1>^)2  =     9 

(2K  n)^  +     (>^)'  =  19 

9 
10 
15 

(2  >^  1/3)2  +  (1^)2  =  21 

(2K  1/3)2  +  (2^)2  =  25 

(3>^  1^3)2  +     (>^)2  =  37 

for  which  the  number  of  settlements  is  to  be  found,  be  called  /(.    The  problem  is  to 
find  k  and  /. 

First,  find  an  integer  m  such  that   (m  +  1)  (m  —  2)  <  /j  ^  (m  +  1)  (/n  —  2)  +  2m. 
Call  the  expression   (m  +  1)  (771  —  2)  +  2m  =  /?o-   There  are  two  cases: 

2m  —  1                    2in  —  1 
a.    If  ho  —  h  ^  m,  then  fe  =  — and  /  =  — {hg  —  h) 


b.    If  ho  —  /z  >  m,  then 

k  =  m  —  I;  and  /  ==  (m  —  1)  —  {h^  —  h)  . 


-W.  F.  S. 


120  Part  Two.     Ecor.oniic  Regions 

The  most  important  result  of  the  preceding  argument,  however, 
is  that  with  discontinuous  settlement,  the  possible  size  of  the  market 
areas  and  the  number  of  settlements  they  contain  also  grow  dis- 
continuously.  This,  again,  makes  surplus  profits  possible.  For  if 
sales  in  32  settlements,  say,  were  required  to  make  a  certain  com- 
modity profitable,  area  No.  13  with  31  settlements  would  be  too 
small.  But  the  next  area  is  the  unnecessarily  large  market  area  14, 
with  36  settlements,  so  that  sales  must  extend  to  36  settlements. 
The  demand  curve  would  then  intersect  the  cost  curve  instead  of 
merely  touching  it,  and  surplus  profits  would  thus  arise  in  this 
industry."'^^  Such  moderate  surplus  profits  are  actually  the  rule, 
for  it  would  be  pure  chance  if  the  demand  curve  in  its  jumps  should 
still  "  just  touch  the  cost  curve." 

One  more  point  must  be  emphasized.  Not  all  the  possible 
market  areas  need  occur  in  reality.  There  may  not  be  any  com- 
modity whose  commercial  production  would  be  profitable  for  only 
three  farms.  Then  area  1  would  not  exist.  But  conversely,  every 
actual  market  area  must  be  on  the  list  of  possible  ones.^^ 

14.  As  a  consequence  of  this  discontinuity  in  the  size  of  areas  the  demand  curve 
jumps  if  it  is  displaced  toward  the  left  by  a  diminution  of  area  in  the  course  of  the 
Chamberlin  process.  With  mere  price  increases,  on  the  other  hand,  the  demand  falls 
continuously,  if  one  moves  up  along  the  old  curve,  although  a  gradual  price  rise  also 
eliminates  settlements  discontinuously  at  the  shipping  limits  then  prevailing.  This 
apparent  contradiction  is  easily  explained:  Before  a  place  is  suddenly  and  entirely 
eliminated  from  the  sales  area,  its  demand  has  gradually  fallen  to  zero  with  the  rising 
price;  i.  e.,  its  elimination  no  longer  affects  total  demand.  Thus  whether  a  market 
area  is  reduced  by  the  approach  of  competitors,  or  by  rising  prices,  are  two  entirely 
different  questions.  The  discontinuity  of  settlements  has  an  effect  only  in  the  first 
case  because  here,  in  contrast  to  the  second  case,  the  demand  of  settlements  on  the 
borders  is  not  zero. 

15.  They  may  even  soften  the  impact  of  business  cycles  with  continuity  of  settle- 
ment. An  oligopolistic  struggle  for  the  distribution  of  surplus  profit  may  break  out, 
a  discussion  of  which  is  not  warranted  by  the  insignificant  object  of  strife  and  the  even 
distribution  of  chances.  The  solution  of  Frisch,  Schneider,  von  Stackelberg,  Moller, 
Zeuthen,  Palander,  and  others  can  be  adapted  to  the  problem. 

16.  Among  the  first  10  cases  the  realization  of  Nos.  3,  6,  and  8  seems  to  me  especially 
probable.  Here,  in  contrast  to  the  remaining  cases,  no  settlement  is  divided  among 
several  supply  centers.  Various  circumstances  are  against  such  a  partition.  (1)  It 
hardly  occurs  in  administrative  districts,  and  trade  has  a  tendency  to  turn  toward 
political  centers  as  populous  places.  Political  division  is  possible,  however;  one  need 
only   recall   earlier-  conditions,   when    several    lords   had   serfs    in    the   same   villages. 

(2)  Division  would  create,  not  theoretically  but  practically,  an  unstable  economic 
situation:  thiee  competing  for  one  place!  (3)  If  the  settlements  are  single  farms, 
division  is  wholly  improbable.  If  it  does  not  occur  a  no-man's-land  arises  between 
neighboring  market  areas  with  discontinuous  settlement  that  makes  oligopolistic 
market  strategy  even  more  difiBcult. 


Network  of  Markets  181 


§2.  Location  at  a  Center  of  Gravity 

A  production  site  might  be  established  between  three  settle- 
ments instead  of  in  one  of  the  original  settlements.  This  we  shall 
call  location  at  a  center  of  gravity.  Compared  with  location  in  a 
settlement  it  has  the  disadvantage  of  no  local  demand  worth  men- 
tioning, but  the  advantage  of  being  nearer  to  the  next  sales  points. 
Hence  the  smallest  possible  value  for  nF  is  0.58a  instead  of  a,  as  is 
the  case  with  location  in  a  settlement.  Except  for  nV,  however,  the 
two  possibilities  show  an  astonishing  agreement  in  respect  to  the 
size  and  situation  of  the  market  areas.  Thus  all  but  the  last  column 
of  Table  6  is  valid  also  for  location  at  the  center  of  gravity.  On 
the  other  hand,  the  distribution  of  sales  points  within  otherwise 
similar  areas  is  essentially  different.  The  question  of  whether  one 
of  the  two  locations  is  definitely  superior  must  now  be  investigated. 
The  criterion  for  superiority  would  be  that  the  same  number  of 
places  permitted  a  greater  total  demand. 

Unusual  demand  curves  may  be  imagined  that  actually  favor 
one  of  the  locations  throughout;  but  if  the  straight  line  may  be 
regarded  as  the  average  of  all  possible  demand  curves,  it  can  be 
shown  "  that,  at  least  for  the  10  smallest  areas  examined,  location 
at  an  original  settlement  entails  a  greater  demand  in  half  of  the 
cases  (areas  3,  4,  6,  7,  and  9) ,  and  location  at  a  center  of  gravity  in 
the  other  half.^^  However,  in  those  cases  where  location  at  the 
center  of  gravity  is  more  economical,  its  advantage  over  location  in 
a  settlement  is  more  pronounced  than  the  reverse. 

Thus  whereas  location  sometimes  appears  more  favorable  in  a 
settlement  and  sometimes  at  a  center  of  gravity,  if  each  is  con- 
sidered by  itself  it  may  be  presumed  that  when  everything  is  carefully 
considered  location  uniformly  at  either  one  site  or  the  other  is  to  be 
preferred  on  the  whole  for  many  reasons.  (1)  With  a  split  location 
structure  the  number  of  industrial  sites  would  increase,  and  con- 
sequently  the   advantage  of  a   concentrated   local   demand   would 

17.  The  proof,  though  not  difficuh,  is  too  long  to  be  given  here.  In  any  case,  it  is 
unimportant  for  the  development  of  our  ideas. 

18.  Consequently  it  may  happen  that  with  appropriate  location  of  a  factory  fewer 
places  will  provide  a  greater  demand  for  the  same  commodity.  This  is  possible  with 
goods  whose  longest  shipping  distance  is  too  short  to  make  the  demand  at  points  on  the 
borders  of  the  large  area  felt,  either  strongly  or  to  any  degree,  so  that  the  more 
favorable  situation  of  the  remaining  places  in  respect  to  the  factory  is  decisive  in  the 
small  area.  With  relatively  short  shipping  distances  other  unusual  features  may 
appear,  but  their  discussion  would  lead  us  too  far  afield. 


128  Part  Two.    Economic  Regions 

decrease.  This  is  especially  true  of  economic  capitals,  which  deter- 
mine the  sites  of  other  locations,  as  we  shall  see  later.  (2)  The 
splitting  of  towns  would  also  bring  about  a  splitting-up  of  transport 
lines.  (3)  With  larger  areas  the  advantage  of  one  situation  over 
another  is  negligible;  with  the  smallest  ones  it  is  greatest  for  areas 
1  and  3. 

Above  and  beyond  all  this  there  is  a  number  of  practical  reasons 
why  the  uniform  pattern  of  locations  will  generally  favor  original 
settlements.  (1)  Industry  first  arose  as  a  side  occupation,  or  as 
production  on  a  socage  farm  or  in  a  village.  (2)  Location  in  a 
settlement  assures  better  contact  with  consumers.  (3)  Lines  of 
communication  even  between  economically  self-sufficient  settlements 
are  already  in  existence,  but  may  have  to  be  provided  for  locations 
at  a  center  of  gravity. 

c.     REGIONAL    NETWORKS 

We  have  seen  that  there  is  only  one  suitable  shape  for  market 
areas,  and  only  a  limited  number  of  possible  sizes  and  situations. 
Because  of  the  restricted  number,  the  most  favorable  area  is  uniquely 
determined  for  every  commodity.^^  One  and  the  same  area  will 
usually  be  the  market  for  several  goods,  since  there  are  more  products 
than  regional  sizes.  But  beyond  the  market  area  these  goods  need 
have  nothing  in  common.  In  particular,  they  will  generally  realize 
sales  of  entirely  different  magnitude,  even  though  local  demand  at 
the  factory  price  is  the  same,  since  even  with  the  same  market  area 
they  will  generally  have  different  possible  shipping  distances.  In- 
deed, one  might  almost  establish  the  rule  that  goods  having  one  of 
these  three  properties  in  common— market  area,  possible  shipping 
distance,  and  necessary  sales  volume— will  differ  in  respect  to  the 
two  others.-"  Thus  with  a  discontinuous  distribution  of  population 
things  are  no  longer  as  they  are  with  a  continuous  distribution, 
where  every  product  can  be  as  unfailingly  recognized  by  its  area  as 
the  chemical  elements  by  their  specific  weights.  But  now  the  forms 
can  be  deduced  a  priori  in  which  the  sale  of  all  known  goods  and 

19.  With  a  discontinuous  population  the  number  of  settlements,  not  the  size  of 
the  area,  must  be  as  small  as  possible. 

20.  From  this  a  few  apparent  anomalies  follow.  For  example,  even  with  the  same 
local  demand  at  the  factory  the  total  demand  over  a  small  region  may  exceed  that 
throughout  a  larger  one.  This  is  easily  possible  when  the  product  sold  in  the  smaller 
area  has  a  longer  maximum  shipping  distance.  The  greater  the  possible  shipping 
distance,  the  fewer  settlements  will  be  required  to  achieve  a  certain  sales  volume,  for 
a  long  distance  implies  little  sensitivity  to  shipment;  that  is,  only  an  inconsiderable 
fall  in  demand  with  increasing  distance. 


Network  of  Markets  123 

of  all  others  still  to  come  must  take  place.  Market  areas  are  no 
longer  specially  tailored  for  a  single  commodity,  but  the  commodity 
takes  the  most  suitable  size  from  a  fixed  assortment.  We  can  there- 
fore continue  our  deductions  without  first  considering  the  actual 
sales  situations  for  the  various  goods.  The  actual  must  be  con- 
tained in  the  possible. ^^ 

Market  areas  need  no  longer  be  classified  according  to  goods, 
therefore,  but  according  to  size.  Goods  whose  necessary  market  areas 
are  equal  are  included  in  one  class.  Because  of  their  shape  the 
areas  of  the  same  size  lie  in  immediate  contact  with  one  another, 
and  form  a  honeycomb  network  that  covers  the  whole  area.  Their 
centers,  that  is,  the  production  sites  for  the  same  commodity  classes, 
are  all  separated  from  one  another  by  the  minimum  distances,  2p, 
and  are  distributed  in  regular  honeycomb  fashion.  But  how  are 
production  sites  for  different  classes  of  goods  situated  with  respect 
to  one  another? 


21.  What  can  be  deduced  need  not  be  derived  laboriously  yet  imperfectly  from 
experience.  Here  I  disagree  with  Euckens,  Grundlagen  der  Nationaloknonomie  (1940) , 
p.  126.    On  the  contrary,  reason  opens  new  possibilities  that  fructify  daily  experience. 


Chapter  11.     The  System  of  Networks 


a.     THE    GENERAL    PATTERN 

Market  areas  for  the  various  kinds  of  goods  resemble  narrow- 
meshed  or  wide-meshed  nets  of  hexagons  that  to  start  with  can  be 
thrown  at  will  over  our  plain. ^  Despite  the  resulting  confusion, 
every  place  would  lie  in  the  market  area  of  every  good.-  Yet  it  is 
worth  while  to  bring  order  out  of  this  chaos  by  means  of  a  few 
reflections. 

First,  we  lay  the  nets  so  that  all  of  them  shall  have  at  least  one 
center  in  common.  Here  a  metropolis  will  arise,  with  all  the  advan- 
tages^ of  a  large  local  demand.  Second,  we  turn  the  nets  about 
this  center  in  such  a  way  as  to  get  six  sectors  with  many  and  six 
with  only  a  few  production  sites  (Figs.  28  and  29)  .*  With  this 
arrangement  the  greatest  number  of  locations  coincide,  the  maxi- 
mum number  of  purchases  can  be  made  locally,  the  sum  of  the 
minimum  distances  between  industrial  locations  is  least,  and  in 
consequence  not  only  shipments  but  also  transport  lines  are  reduced 
to  a  minimum.  With  discontinuous  settlement,  of  course,  only  the 
networks  of  those  market  regions  described  on  page  1 1 7  as  lying 
obliquely  can  be  rotated.  Figure  27  shows  that  there  are  always 
two  possibilities  for  their  location.  If,  for  example,  a  circle  with 
the  diameter  of  area  3  as  radius  be  drawn  about  the  central  town, 
it  will  pass  in  the  first  quadrant  through  three  settlements,  which 
are  thus  possible  locations  for  centers  of  the  neighboring  area  3. 
There  is  now  a  choice  between  the  two  outer  settlements  whose 
distance  is  likewise  equal  to  the  radius  of  the  circle,  or  the  middle 
settlement  together  with  a  fourth  possible  point  at  the  proper  dis- 

1.  With  the  limitation,  aheady  established,  that  their  middle  points  coincide  with 
original  setlements,  not  with  centers  of  gravity  and  certainly  not  with  arbitrary  sites. 

2.  The  situation  is  wholly  symbolic.  We  live  simultaneously  amidst  many  sur- 
roundings and  cannot,  without  harm,  neglect  all  others  for  the  sake  of  one  single 
preference. 

3.  This  presupposes  that  in  a  number  of  branches  the  planning  curve  does  not  fall 
steadily.   See  Figure  48  and  the  accompanying  text. 

4.  More  places  are  indicated  in  Figure  29  than  in  Figure  28,  which  shows  only  the 
centers  of  the  four  smallest  areas,  whereas  Figure  29  shows  all  regions. 

124 


The  System  of  Nclivorks 


125 


tance  in  the  next  quadrant— not  with  one  of  the  other  two,  which 
are  too  near.  Once  network  3  is  selected,  the  choice  as  to  position 
of  the  remaining  networks  that  can  be  rotated  is  no  longer  free, 


Fig.  28.  Theoretical  pattern  of  an 
economic  landscape 


Fig.  29.  Theoretical  pattern  of  an 
economic  landscape,  but 
without  nets 


Fig.  30.  Indianapolis  and  environs  within 
a  radius  of  60  miles.  (From  Andree's 
Handatlas,  8th  ed.,  p.  198.) 


Fig.  31.    Toledo  and  environs  within  a 
radius  of  60  miles.    {Ibid.) 


provided  the  separation  into  sectors  with  many  or  few  towns  is  to 
be  carried  through.  Depending  on  the  decision  as  to  the  position 
of  area  3,  the  middle  or  two  outer  sectors  in  the  first  quadrant  will 
contain  but  few  towns. ^    The  cogwheel-shaped  immediate  environs 


5.  The  following  consideration  makes  this  clear:  In  Figure  27  the  middle  and  lower 
sectors  of  the  first  quadrant  are  mirror  images  of  one  another  in  respect  to  possible 


J26  Part  Two.    Economic  Regions 

of  the  metropolis  are  also  necessarily  poor  in  towns,  for  only  a 
few  local  goods  can  be  produced  with  profit  in  its  neighborhood. 

Neither  are  the  outlying  environs,  even  within  the  same  sector, 
uniformly  settled.  Some  localities  have  no  production  of  their  own 
at  all,  whereas  at  other  places  the  centers  of  several  market  areas 
of  varying  size  coincide.  Such  agglomerations  of  locations,  or  "  cen- 
tral sites,"  as  Christaller  so  appropriately  calls  them,  are  found  upon 
closer  examination  to  be  distributed  with  a  certain  regularity  (Fig. 
32) .  Smaller  agglomerations  can  be  found  at  distances  of  V3a,  Sa, 
and  2V^  from  each  other;  many  of  medium  size  at  distances  of  6a; 
and  larger  ones  lie  1 2a  apart.^  Yet  it  is  not  true  that  when  an  equal 
number  of  areas  have  their  centers  at  two  places  these  areas  them- 
selves will  be  of  equal  size.  Towns  of  the  same  size  may  quite 
possibly  fulfill  entirely  different  economic  functions;  that  is,  they 
can  harbor  entirely  different  industries.  A  smaller  agglomeration 
generally  lies  about  halfway  between  two  larger  ones.  The  size  of 
agglomerations  increases  with  their  distance  from  the  metropolis. 

The  greater  the  accumulation  of  industries  the  cheaper,  ob- 
viously, are  industrial  goods  on  the  average.  Their  wholesale  price 
level  is  therefore  lowest  in  the  metropolis.^  In  the  ring  containing 
few  towns,  and  somewhat  farther  out,  industrial  prices  rise  sharply 
until  at  last,  with  minor  fluctuations,  production  sites  again  become 
so  numerous  that  the  local  price  level  falls  (unless  the  index  is 
heavily  weighted  with  goods  having  a  very  large  sales  area  that  can 
be  purchased  only  in  the  metropolis  and  therefore  become  increas- 
ingly dear  with  rising  freight  costs)  . 

If  the  entire  regional  system  has  the  radius  L,  goods  for  which 
p  is  somewhat  greater  than  L/2  can  be  produced  only  in  the  metrop- 
olis.^ Even  locations  on  the  borders  between  two  regional  systems 
can  no  longer  compete  in  such  commodities.  Consequently,  at  a 
distance  of  something  more  than  L/2,  no  new  competition  arises 
for  the  metropolis.    With  a  distance  of  something  more  than  L/2, 


locations.  On  the  other  hand,  the  distance  between  these  pairs  of  possible  locations  is 
less  than  the  radius  of  the  circle  on  which  they  lie.  Hence  they  are  too  near  together, 
and  a  choice  must  be  made  between  them.  If  a  location  in  the  lower  sector  is  chosen, 
its  mirror  image  in  the  middle  sector  must  necessarily  be  relinquished.  The  possible 
locations  in  the  two  outer  sectors,  on  the  contrary,  are  separated  by  the  proper  distanc^^. 

6.  The  minimum  distance  between  two  production  centers  of  any  given  size  is  aV3, 
and  every  center  has  at  least  one  neighbor  at  this  distance. 

7.  Living  costs,  on  the  other  hand,  which  include  agricultural  products,  rent,  and 
extra  expenses,  and  take  retail  markups  into  account,  are  highest  in  the  metropolis, 
at  least  when  fuel  is  disregarded  for  reasons  discussed  on  p.  42,  note  10. 

8.  Such  a  typical  metropolitan  function,  for  example,  is  bank  clearing  at  the  highest 
level. 


The  System  of  Networks 


127 


^\/5     1^  V/  J 


7\^i  Y^  0^  V  ^^^f^ I  Y  ^^ 


2     J     5    5    z    11 

V/      >i.v 


_« — 9 — 


7i,i^ — 4 o-.te. — «L «__3oc — • «-• 


V  V   \^  v/  ^^ 
»... »    »    >   ^- 


s\i^:...-^j3__iz 


?j  • 


.i^':..t-#-:-,-- 


/\i.</ 


"750 

Fig.  32.     The  transport  lines  in  the  ideal  economic  landscape    (one  sector  only)  . 

The  numbers  refer  to  the  number  of  centers  which  coincide  in  a  particular  point. 
In  the  middle  of  the  landscape  there  aie  150  centers  of  areas  all  of  which  are  smaller 
than  the  landscape  to  which  the  pictured  sector  belongs. 

The  lines:  The  number  of  centers  along  the  heavy  lines  is  twice  or  more  that  along 
the  broken  lines;  the  number  of  centers  along  the  thin  lines  is  approximately  one  and 
a  half  times  the  number  along  the  broken  lines.  The  difference  in  traffic  density 
betM'een  the  left  city-rich  and  the  right  city-poor  sector  can  easily  be  seen. 


128 


P(nt.  Txuo.     Economic  Rarions 


11. 


^     f4 


•       1.33     •S'       'i       1.39    ^/      ^       ll 


28       23 


31        32       35/.     15 


1*10    2*8       •       '••'      9'       Z*^^     •       ^* 


2?.       /i,      25       26      W       6  16      , 

•       1*t       •         •        Ipll      •         •       ^mq    3 


w 


,  20        21      21/  12  n\ 

15       16        n     ,  /..      8  13  > 

■•     ,       «        13       n/5  2         9  6      .37j^ 

8        8     fn/  6  iVy^ 

f.|    fi.      ./     ,.     2*       .i,.f 

•       /i         •        •       IjtiZ 
f9       24        m 


Z 


Fig.  33.    Location  of  regional  centers  in  the  complete  system. 
The  centers  bear  the  numbers  of  their  region. 


Fig.  34.  Regions  with  equal  structure.  (I)  A  =  3.  Every  town  controls  two  complete 
towns  of  the  next  lower  rank.  The  numerals  indicate  regional  centers  with  the  same 
number  as  in  Figure  33,  from  which  this  one  was  made  by  omitting  all  regions  without 
a  center  and  two  complete  places  of  next  lower  rank. 


The  System  of  Networks  129 

prices  will  thus  rise  again,  since  goods  with  a  large  sales  radius 
become  more  expensive  with  increasing  freight,  and  their  (uni- 
lateral) price  rise  cannot  be  counteracted  by  local  production.  Thus 
from  the  metropolis  to  the  boundaries  of  its  region  we  find  whole- 
sale prices  first  low,  then  rising,  then  falling,  and  finally  rising 
again.^'^° 

Finally,  upon  drawing  in  the  principal  lines  of  communication, 
we  find  that  the  busiest  traffic  (measured  by  the  number  of  area 
centers  per  unit  of  length)  occurs  along  the  sectors.  Thus  twelve 
such  main  lines  radiate  from  the  metropolis;  "  i.  e.,  six  lines  cross 
in  it.  Elsewhere  in  the  region  there  are  junctions  of  only  two  or 
three  lines.  Cross  connections  in  the  vicinity  of  the  metropolis  are 
theoretically  not  worth  while  and  seldom  exist  in  practice.^^  In 
sectors  containing  but  few  towns,  the  lines  of  communication  are 
fewer  and  generally  not  well  developed.  In  an  over-all  view,  they 
spread  out  like  a  cobweb  around  the  metropolis. 

Order  has  now  suddenly  been  brought  into  our  market  areas. 
The  position  of  individual  regional  networks  is  no  longer  a  random 
one,  but  follows  from  economic  principles.  Now  we  realize  that 
there  must  be  at  least  one  metropolis,  around  which  its  market  area 
and  competing  locations  lie  concentrically."    It  is,  so  to  speak,  the 

9.  Instead  of  spatial  price  differences  tfiere  are  spatial  differences  in  profits  wtien  a 
government  enforces  the  same  prices  everywhere.  For  any  individual  product  the 
"  crater  field  "  of  price  is  then  replaced  by  profit  "  cones." 

10.  This  is  one  reason  why  it  is  generally  meaningless  to  speak  of  the  price  level 
of  a  region;  the  dispersion  of  local  prices  around  the  average  for  the  whole  region  is 
too  great.  The  price  cones  and  price  funnels  about  single  points  of  supply  and  pro- 
duction give  rather  the  impression  of  a  mountain  range.  We  shall  encounter  the  other 
reason  later:  not  only  the  height,  but  also  the  change  in  prices  varies  locally  too  much. 
To  conceal  these  variations  by  calculating  their  average  would  lead  to  error  in  many 
cases. 

11.  Eleven  through  railway  lines  run  out  from  Berlin,  for  instance;  from  Paris, 
including  branches  within  a  radius  of  about  25  miles,  exactly  twelve;  directly  from 
London,  twelve  through  highways.  This  orientation  of  main  arteries  toward  the 
metropolis  was  noticeable  after  the  incorporation  of  Austria  and  the  Sudetenland  into 
the  Reich.  Their  main  roads  formerly  ran  toward  Vienna  and  Prague,  and  good  con- 
nections with  the  old  Germany  were  often  possible  only  by  way  of  their  own  capital 
cities. 

12.  In  endeavoring  to  travel  by  railroad  around  Munich  or  Nuremberg,  say,  one 
finds  that  this  is  possible  only  at  a  distance  of  some  50  miles. 

13.  Further  important  results  are:  six  sectors  containing  few  towns  and  six  con- 
taining many  are  grouped  about  the  metropolis;  in  its  immediate  environs  a  region 
having  the  form  of  a  cogwheel  remains  free  of  towns;  the  towns  show  a  honeycomb 
distribution,  and  are  separated  from  one  another  by  the  same  minimum  distance;  the 
main  lines  of  communication  meet  in  the  metropolis;  and  so  on. 


joQ  Part  TtL'o.     Economic  Regions 

industrial  corollary  of  Thiinen's  "  isolated  state."  We  shall  not 
apply  this  political  concept  to  a  situation  that  is  at  first  entirely 
nonpolitical,  but  shall  call  this  system  of  market  networks,  this 
highest  phenomenon  in  the  hierarchy  of  economic  spatial  arrange- 
ment, exactly  what  it  is:  an  economic  landscape.^* 

b.     SPECIAL    CASES 
§1.     Market   Areas   of   Similar   Structure 

It  has  already  been  mentioned  that  our  series  of  market  area 
includes  all  cases  that  are  logically  possible,  though  not  all  need 
exist  in  reality.  They  cannot  exist,  either  because  there  is  no  product 
whose  necessary  market  area  is  exactly  as  large,  or  because  extra- 
economic  factors— above  all,  political  division  into  administrative 
units— influence  spatial  economic  arrangement. 

Political  division  is  frequently  carried  out  in  such  a  way  that  a 
certain  number  of  smaller  regions  are  combined  into  a  larger 
administrative  district.  In  France,  for  example,  three  cantons  make 
an  arrondissement  and  three  arrondissements  a  departement.  We 
shall  therefore  briefly  examine  regional  systems  in  which  every  area 
includes  k  regions  of  the  next  smaller  size.^^  All  other  regions  that 
are  possible  according  to  our  analysis  will  accordingly  be  disregarded. 

If  k  =  ^,  say.  Tables  6  and  7  show  that  regional  sizes  I,  4,  II, 
30,  and  so  on  may  exist,  but  not  2  and  3,  5  and  10,  and  12  to  29. 

14.  Economic  empire,  economic  region,  or  economic  area  (in  the  narrower  sense) 
would  be  suitable,  especially  if  one  recalls  the  original  meaning  of  regio  and  Gebiet: 
an  area  of  authority,  according  to  Grimm's  Worterbuch.  It  is,  in  fact,  the  economic 
domain  of  the  central  metropolis.  On  the  other  hand,  economic  district,  or  province, 
emphasizes  the  lack  of  self-sufficiency  that  is  generally  encountered  in  reality.  Geog- 
raphers may  object  to  the  way  in  which  I  employ  the  word  landscape,  but  I  ask  them 
to  consider  that  it  not  only  corresponds  with  common  usage,  but  approaches  very 
closely  the  true  meaning  of  the  word.  In  both  cases  the  environs  relate  to  a  center— 
the  beholder,  or  the  metropolis.  Only  by  way  of  these  economic  relationships  do 
geographic  peculiarities  influence  the  region  that  has  sprung  out  of  pure  space,  as 
with  R.  Hapke's  more  general  "  economic  landscape  "  ("  Die  okonomische  Landschaft 
und  Gruppenstadt  in  der  alteren  Wirtschaftsgeschichte,"  in  Sozial-  und  Wirtschafts- 
geschichte,  Geddchtnisschrift  fiir  G.  von  Below,  1928,  pp.  82-104)  .  On  the  other  hand, 
the  "  industrial  landscape  "  of  E.  Winkler,  who,  following  the  general  usage  of  geog- 
raphers, would  orient  all  geography  toward  the  landscape  as  its  sole  object,  represents 
a  geographical  unit  in  which  industry  alone  dominates  ("  Stand  und  Aufgaben  der 
Induslriegeographie,"  Zeitschrift  fiir  Erdkunde,  IX,  597  ff .  [extensive  bibliography].  Also, 
E.  ^Vinkler,  "  Raumordnung  der  Wirtschaft,"  Neue  Ziircher  Zeitung,  October  18,  1940; 
and  in  correspondence.) 

15.  These  regions  may  also  be  pieced  together  from  parts  of  others.  Strictly  speaking, 
therefore,  the  large  region  includes  k  centers  of  next  smaller  regions,  which,  however, 
are  made  up  of  parts  of  more  than  k  such  regions. 


TI>e  System  of  Networks 


131 


For  only  region  No.  4  is  large  enough  to  embrace  three  regions 
No.  1;  only  region  No.  11  embraces  three  regions  No.  4,  and  so  on. 
Table  8  gives  for  a  few  values  of  k  the  most  important  data  for  the 
corresponding  regions. 

Table  8.    REGIONS   WITH   HOMOGENEOUS   STRUCTURE 


Regional 

Size 
(actual) 

Distance  of  the  Centers  from 
Each  Other 

Regional  Size,  Number  in 
the  Complete  System 

k  =  3 

k  =  4 

k  =  7 

k  =  3 

k  =  4 

k  =  7 

1 

afsi 

a  1/41 

ai/;; 

1 

2 

3 

2 

a  1/32 

a  1/42 

a  1/72 
a  1/73 

a  1/76 
a|/7T 

4 

7 

19 

3 

a  1/38 

ay43 

3^45 
a  1/46 

al/4T 

11 

24 

106 

4 

.f^' 

30 

81 

? 

5 

a  1/35 

77 

? 

? 

6 

a  1/38 

? 

? 

? 

7 

.^v 

? 

? 

? 

a  =  distance  of  the  original  settlements,  k  =  number  of  next  smaller  sub-areas.  The 
number  under  the  radical  sign  is  at  the  same  time  the  total  number  of  settlements  in 
the  region  concerned. 

Figures  34  to  36  show  how  much  simpler  the  spatial  picture  is 
than  in  the  complete  system  of  regions.  This  simplicity  is  gained 
by  some  sacrifice  of  economy,  to  be  sure,  since  it  seems  certain  that 
the  necessary  market  areas  of  many  goods  have  sizes  that  do  not 
appear  here.  Such  goods  have  unnecessarily  large  markets  in  a  sim- 
plified system. ^^  Nevertheless,  such  a  simple  landscape  has  something 


16.  Hence  it  is  not  correct  to  regard  the  special  case  where  A  ^  3  as  "  the  "  arrange- 
ment according  to  the  principle  of  most  efficient  supply,  as  does  Christaller,  Die 
zentralen  Orte  in  Siiddeutschland  (Jena,  1933) ,  pp.  63-85.  Furthermore,  the  chance 
fact  that  when  /t  =  3  all  places  lie  symmetrically  with  respect  to  each  of  the  six  through 
lines  and  hence  no  thickly  and  thinly  settled  areas  appear,  has  misled  him  into  estab- 
lishing a  different  arrangement  on  the  "  communication  principle  "  (ft  =  4)  .  In  this 
arrangement  the  greatest  possible  number  of  important  places  lie  on  main  lines  of 
communication.  But  this  is  true  anyway  (see  Fig.  32) ,  especially  in  a  complete  system 
of  market  regions.  The  communication  principle  was  one  of  the  axioms  by  which 
the  final  position  of  regional  networks  was  determined.  In  our  economic  landscape 
both  this  principle  and  the  principle  of  supply  are  therefore  united.  It  would 
disrupt  logical  geometrical  development  if  one  were  to  suppose  that  cheapness, 
rapidity,  frequency,  and  extent  of  communication  over  long  distances  could  create  a 
special   locational   advantage   that  would   result   in   more  industries   being  established 


132 


Part  Two.    Economic  Regions 


attractive  about  it,  and  above  all  it  is  probably  the  most  that  can 
be  attained  today  by  conscious  planning.  Adapted  to  individual 
cases  it  forms,  furthermore,  the  very  basis  for  the  new  organization 
in  the  East. 


y 


o  \  o       o  /  o 

y —  \               / 

O/O  o\o        of 

o/o        ®  O/O         o.o 

o  \    O  O    / 

V— — ^v  / 

•         O/O  o\o         «'" 


,-'-< 


Fig.  35.  Regions  with  equal  structure. 
(2)  /t  =  4.  Every  town  dominates  three 
complete  towns  of  next  lower  rank.  In 
contradistinction  to  Figure  34,  regional 
boundaries  and,  instead  of  one  sector,  the 
whole  interior  of  the  landscape  have  been 
drawn. 


Fig.  36.  Regions  with  equal  structure. 
(3)  k  =  l.  Every  town  dominates  six  com- 
plete towns  of  the  next  lower  rank. 


than  otherwise  would  be  the  case;  partly  because  they  could  manage  with  smaller 
regions,  partly  because  these  regions  would  be  narrower  in  the  direction  of  the  com- 
munication line  and  therefore  broadened  at  right  angles  to  it. 

Whoever  wishes  to  take  all  this  into  account  must  either  incorporate  it  in  the 
general  location  equations  or  content  himself  with  a  partial  geometrical  presentation. 
In  any  case,  he  has  to  forego  the  advantages  of  a  complete  geometrical  presentation. 
For  the  same  reason  we  did  not  consider,  among  other  things,  the  fact  that  in  the  role 
of  important  consumers  towns  mutually  distort  their  own  market  regions.  For  instance, 
the  smaller  towns  are  displaced  excentrically  in  their  regions  toward  the  larger,  as  is 
rightly  considered  by  Culemann  in  his  planning  ("  Zur  Stadtplanung  in  den  neuen 
deutschen  Ostgebieten,"  Raumforschung  und  Raumordnung,  1941,  pp.  100-230) .  With 
larger  towns  it  is  supposed  that  the  local  demand  and  the  demand  from  the  environs 
can  be  met  by  separate  regions;  this  justifies  the  assumption  that  the  market  region 
for  a  given  product  will  be  as  large  as  in  smaller  places. 

The  special  case  ft  =  7  is  called  by  Christaller  {op.  cit.,  pp.  84-85)  a  structure  based 
on  the  administrative  principle.  He  aptly  characterizes  it  by  the  fact,  first,  that  no 
place  is  divided  among  several  administrative  districts  (as  is  often  the  case,  of  course, 
with  twin  cities  like  Ulm  and  Neu  Ulm,  or  Kansas  City,  Missouri,  and  Kansas  City, 
Kansas)  ;   secondly,  that  the  market  regions  of  the  places  in  question  are  cut  up  as 


The  System  of  Networks  133 

§2.     Square   Market   Regions 

We  have  already  found  the  second  best  market  region  to  be  the 
square."  In  utilizing  demand  it  frequently  is  not  much  inferior 
to  the  hexagon  and  has  the  advantage  of  simply  drawn  boundaries, 
but  also  the  disadvantage  of  longer  roads.  In  the  square,  too,  the 
relation  between  the  number  of  settlements,  the  size  of  market  areas, 
and  the  distance  of  their  centers  is  extremely  simple.  If  a  be  the 
minimum  distance  separating  the  original  settlements  (which  is 
perhaps  5  per  cent  less  with  a  square  than  with  a  honeycomb  dis- 
tribution) and  n  the  number  of  settlements  in  a  market  region, 
the  size  of  the  region  is  a-n  and  the  distance  of  its  center  from  the 
nearest  rivals  a  V"— exactly  as  in  the  honeycomb  shape.  The  smallest 


little  as  possible  by  political  boundaries.  For  these  conditions  ft  =  7  is,  in  fact,  a 
possible  solution;  ft  =  13  would  be  another.  In  the  first  case,  however,  the  regional 
boundaries  are  not  as  Christaller  has  drawn  them,  but  as  they  appear  in  our  Figure  36. 
Christaller's  figure  is  possible  only  because  he  departs  from  the  most  rational  distribu- 
tion of  the  original  settlements.  Besides,  the  political  principle  does  not  contradict 
the  economic  principle,  as  he  believes;  rather,  a  few  of  the  possible  market  boundaries 
are  at  the  same  time  possible  political  boundaries. 

The  complete  regional  system  considers  all  principles  at  once.  Whenever  only  the 
smallest  possible  market  areas  of  similar  structure  are  taken  into  account  despite  their 
slight  flexibility  (as  is  often  done  in  practical  spatial  planning  for  the  sake  of  sim- 
plicity) ,  each  of  the  three  smallest  regional  types  is  especially  advantageous  from  a 
different  standpoint.  Thus  ft  ^  3  is  really  the  best  solution  according  to  the  supply 
principle,  because  under  these  circumstances  it  still  provides  the  largest  assortment  of 
regions;  ft  =  4  is  the  best  according  to  the  communication  principle,  and  ft  =  7 
according  to  the  political  principle.  In  this  sequence  the  central  sites  become  less 
numerous  and  larger  and  the  whole  system,  of  course,  cruder  and  more  rigid.  Yet 
although  Christaller  has  limited  himself  to  these  special  cases,  his  inquiry  is  the  best 
that  I  know  in  all  the  literature  on  the  subject,  and  at  the  same  time  a  distinguished 
example  of  research  in  economic  geography.  It  has  visibly  influenced  planning  in  the 
East  (see,  for  example,  Reichskommissar  fUr  die  Festigung  deutschen  Volkstums. 
Stabshauptant.  Planung  und  Aiifbau  im  Osten  [Berlin,  1941],  7.  Hauptdorfbereiche 
bei  Kutno) . 

That  not  only  the  subject,  but  also  the  manner  of  its  presentation,  fit  so  perfectly 
into  our  own  system  is  the  more  remarkable  in  that  the  present  system  was  developed 
without  knowledge  of  his. 

17.  Thiinen  assumes  it  as  an  example  (Der  isolirte  Staat  in  Beziehung  auf  Land- 
wirtschaft  und  Nationalokonomic  [Hamburg,  1826;  Schumacher-Zarchlin  edition,  Berlin, 
1875],  Vol.  II,  Pt.  II,  §4,  p.  11),  and  C.  Culeraann  ("  Aufbau  und  Gliederung  gebiet- 
licher  Bereiche  als  Aufgabe  raumlicher  Gestaltung,"  Raumforschung  und  Raum- 
ordnung,  1942,  pp.  249-256)  recommends  the  rectangle  because,  unlike  the  hexagon, 
through  lines  of  communication  do  not  cut  up  small  regions  and  thus  disturb  local 
traffic,  but  run  tangent  to  them.  Nevertheless,  either  long  detours  often  result  or  else, 
as  in  many  cities,  diagonal  streets  are  subsequently  laid  out,  so  that  the  regions  are 
cut  up  after  all. 


134 


Part  Two.     Economic  Regions 


regions  include  2,  4,  5,  8,  9,  13,  16,  etc.,  settlements,  thus  increasing 
in  size  rather  quickly  as  in  the  honeycomb  form.  Here,  too,  there 
is  a  choice  as  to  how  a  few  regions  (Nos.  3,  6,  9,  etc.)  shall  be  placed, 
and  with  proper  positions  sectors  are  likewise  obtained  that  are  rich 
or  poor  in  towns;  four  per  quadrant  in  all.    However,  they  are  con- 


2 

t 

12 

i  ^l 

10 

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V 

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5 

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& 

■ 

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j4' 

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5 

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10 

i 

SI/ 

f 

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l/^„5 

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5 

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n 

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5r 

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a 

Fig.  37.  Part  of  a  square  economic  landscape.  Upper 
right  quadrant.  The  central  site  of  the  landscape  and  the 
ten  smallest  regions  surrounding  it  are  in  the  lower  left 
corner.  The  original  settlements  bear  the  numbers  of  the 
ten  smallest  regions  whose  centers  they  are.  Comparison 
with  Figure  32  shows  the  difference  between  quadratic  and 
hexagonal  arrangement.  In  the  former  up  to  eight,  in  the 
latter  up  to  twelve,  routes  run  together  at  one  point.  The 
angles  at  which  they  meet  are  45°,  30°,  or  a  multiple 
thereof.  Thus  right-angled  intersections  occur  in  the  hex- 
agon also,  and  oblique-angled  in  the  square. 

siderably  less  pronounced  than  in  the  hexagon— one  more  reason 
why  square  regions  are  less  economical.  Figure  37  shows  the  shape 
and  the  distribution  of  the  centers  for  the  10  smallest  regions. 

The  cut  shows  the  most  important  lines  of  communication  as 
well.  In  the  larger  places  four  through  lines  intersect;  in  the  smaller, 
two.  But  although  two  square  road  networks  that  are  turned  45 
degrees  in  respect  to  one  another  are  superimposed,  most  connections 
in  the  honeycomb  road  network  are  obviously  shorter   (Fig.  32) . 


Chapter  12.     The  Network  of  Systems 


a.      THE    RELATION    OF    LANDSCAPES    TO    ONE    ANOTHER 

In  comparison  with  the  size  of  our  plain,  even  the  largest  neces- 
sary market  area  may  be  small.  The  landscape  is  not  smaller  than 
this  largest  market  region,  for  this  would  mean  abandoning  without 
cause  the  production  of  goods  with  a  large  necessary  shipping  dis- 
tance. But  the  landscape  will  hardly  become  larger,  for  this  would 
mean  that  all  places  farther  away  than  L    (see  p.    126)    from  the 


Figs.  38  and  39.  Location  of  landscapes  in  respect  to  one  another.  Double  lines: 
connecting  routes  between  large  cites.  Broken  lines:  landscape  boundaries.  Hatched: 
sectors  with  many  towns 


metropolis  //i  would  have  to  give  up  without  reason  the  establish- 
ment of  a  second  metropolis,  Hz.  In  these  distant  parts  the  advan- 
tages of  agglomeration  of  producers  at  //i  are  no  longer  noticeable, 
since  they  buy  nothing  more  from  there;  secondly,  the  difference 
between  sectors  rich  and  sectors  poor  in  towns  and  the  advantages 
of  communication  associated  therewith  disappear  progressively. 
Hence  a  second  metropolis  arises  at  a  distance  of  2L  from  the  first, 
and  so  on,  until  finally  the  entire  plain  is  filled  with  landscapes. 
When  these  have  become  numerous  enough,  they  assume  the 

135 


ig5  Part  Two.     Economic  Regions 

shape  of  regular  hexagons.  But  it  is  still  undecided  how  the  sectors 
with  many  towns  in  the  various  landscapes  lie  in  respect  to  one 
another.  Figures  38  and  39  give  two  possible  solutions.  The  first 
has  the  advantage  that  the  trunk  lines  of  communication,  between 
Hi,  Ho,  and  H^,  run  straight  as  a  string,  and  yet  along  the  route 
containing  the  largest  number  of  towns.  In  the  second  case,  only 
a  few  towns  lie  directly  on  the  main  lines,  but  many  lie  within  a 
relatively  short  distance  to  the  right  or  left  of  them.  It  might  be 
thought  at  first  that  the  position  of  the  largest  market  region  would 
determine  the  boundaries  of  the  entire  landscape,  but  the  demands 
of  communication  are  much  too  imperative  for  them  not  to  pre- 
dominate over  it. 

b.    THE    BOUNDARY    REGION 

All  industries  find  at  least  one  location  in  every  landscape.  Only 
those  goods  with  a  necessary  shipping  distance,  p,  that  is  not  much 
greater  than  L/2  are  produced  at  more  than  one  place.  If  p  lies 
between  a  little  more  than  L/2  and  somewhat  more  than  L/3,  all 
further  locations  will  be  on  or  near  the  boundary  (at  the  most  a 
distance  of  L/3  away  from  it) ,  and  their  market  areas  will  generally 
encroach  upon  the  neighboring  landscape.  But  even  with  goods  for 
which  p  <  L/3  it  is  impossible  that  the  network  of  their  market 
regions  should  end  exactly  at  the  boundary  of  the  landscape.  Empty 
corners  always  develop.  Once  in  a  while,  and  especially  at  a  corner 
where  three  landscapes  meet,  a  factory  erected  on  the  boundary  can 
piece  together  an  adequate  market  region  from  the  empty  corners 
of  neighboring  landscapes.  Should  the  corners  be  too  small  for  this, 
one  of  those  situations  arises  again  in  which  market  regions  can  be 
somewhat  larger  than  necessary  and  moderate  excess  profits  become 
possible,  which  are  particularly  large  in  those  cases  where  L/2  <  p. 
To  summarize:  if  p  is  less  than  L/3,  first  of  all  boundaries  will  be 
transgressed;  if  p  lies  between  L/3  and  L/2,  some  transgression  of 
boundaries  and  some  excess  profits  will  result;  if  p  is  considerably 
larger  than  L/2,  excess  profits  arise. 


u 


These  producers  These  producers 

supply  only  the  domestic  market   |        export  also^ 


These  consumers  These  consumers 

buy  only  domestic  goods  |  import  also 


1.  Only  these,  on  the  other  hand,  can  also  be  displaced  by  foreign  competition. 
Thus  where  a  landscape  boundary  is  at  the  same  time  a  customs  frontier  these  pro- 
ducers alone  are  interested  in  protective  duties  if  they  fear  a  competitive  struggle. 


The  Network  of  Systems  137 

The  effects  of  landscape  boundaries  can  be  more  easily  surveyed 
if  they  are  arranged  not  according  to  the  shipping  distance  of  goods, 
but  according  to  the  locations  of  those  concerned. 

The  area  within  which  consumers  are  affected  by  boundaries  is 
thus  larger  than  the  corresponding  area  for  producers;  that  is,  the 
region  dependent  on  imports  is  larger  than  that  participating  in 
exports.  Of  course,  this  says  nothing  as  to  the  relative  size  of  imports 
and  exports,  though  it  may,  nevertheless,  be  concluded  that  more 
persons  buy  from  abroad  as  consumers  than  export  in  their  capacity 
of  producers.  If  imports  and  exports  are  equal,  the  individual  con- 
sumer imports  less  on  the  average  than  the  individual  producer 
exports. 

c.    RESULTS 

Upon  closer  examination,  many  more  regularities  could  be 
extracted  from  our  system  of  market  regions,  but  as  the  assumptions 
of  our  analysis  are  seldom  completely  fulfilled  in  reality  there  would 
be  little  profit  in  pursuing  it  to  the  last  detail.  The  findings  so  far 
have  been  surprising  enough:  an  area  from  which  our  assumptions 
have  actually  wiped  out  all  differences  can  be  divided  on  purely 
economic  considerations  into  regions  that  do  not  represent  simply 
homogeneous  logical  constructs,  but  form,  if  the  expression  be 
allowed,  an  organic  whole. 

First  we  discovered  simple  market  regions  surrounding  every 
center  of  consumption  or  production  in  the  form  of  a  regular  hexa- 
gon. Second,  for  every  group  of  products  a  net  of  these  market 
regions  was  found.  And  in  the  third  place,  a  systematic  arrange- 
ment of  these  various  nets  appeared.  This  self-sufficient  system  is 
the  ideal  type  of  an  economic  landscape,  or  economic  region  in  the 
narrower  sense.  Finally,  such  landscapes  are  distributed  throughout 
the  world  like  a  network  and  in  accordance  with  definite  laws. 


B.   Economic  Regions  under  Difficult  Conditions 


So  far  we  have  derived  economic  regions  simply  as  functions  of 
distance,  mass  production,  and  competition.  It  must  not,  of  course, 
be  expected  th^t  we  shall  now  consider  all  the  factors  thus  far 
neglected,  in  order  to  derive  a  theory  that  fits  reality.  This  sounds 
good,  but  is  humanly  impossible.  Were  we  to  try,  we  should  either 
end  up  with  equations  and  be  forced  to  give  up  observation  (vis- 
ualization) and  application,  or  else  deal  with  an  infinite  number 
of  individual  cases  without  general  validity.  We  shall  therefore 
discuss  the  effects  of  only  a  few  interesting  changes  from  our  assump- 
tions (Chapters  13  and  14),  and  then  give  conversely  a  more 
realistic  picture  of  economic  regions,  though  without  endeavoring 
to  fathom  all  their  causes  (Chapter  15).  No  simple  rule  for  the 
application  of  theory  to  practice  should  be  expected,  since  that  is 
more  than  science  is  able  to  give.   There  art  and  venture  begin. 


138 


Chapter  13.     Some  New  Factors 

a.    ECONOMIC    DIFFERENCES 
§1.     Local   Differences   in    Price^ 

a.    Within  the  Same  Market  Region 

1.     possibilities   of   geographical   price   policy 

Three  possibilities  are  open  to  the  entrepreneur— for  only  his 
price  policy  will  be  discussed  here.  He  can  adapt  his  prices  to  the 
individual  case  (A)  ;  or  keep  them  so  rigidly  fixed  that  all  buyers 
pay  the  same  f.  o.  b.  price  (F)  or  the  same  c.  i.  f.  (or  "  delivered  ") 
price  (C)  .^-^  Depending  on  his  policy,  his  prices  will  differ  on  the 
average  and  from  place  to  place.  We  shall  now  examine  how  they 
are  set,  how  high  they  are,  and  how  they  affect  the  entrepreneur 
himself  and  his  customers.  In  order  to  do  so  we  must  first  free 
ourselves  completely  from  the  notions  of  traditional  price  theory, 
which  regards  demand  as  though  it  were  concentrated  at  one  point. 

(aa)  Preliminary  Study  (1)  ;  Local  and  Distant  Individual 
Demand— A  Comparison.  Among  other  factors  the  extent  and  vari- 
ability of  the  demand  of  its  consumers  (in  various  places)  will 
depend  on  the  geographic  price  policy  of  a  firm.  For  the  sake  of 
simplicity  we  shall  start  once  more  from  the  assumption  that  indi- 
vidual demand  is  linear,  and  the  same  for  all  individuals. 

1.  Those  who  dislike  mathematics  may  skip  §1  up  to  p.  167.  The  principal 
results  are  these:  (1)  Spatial  price  differentiation  makes  it  possible  to  decrease  the 
size  of  market  areas  still  further.  Hence  it  is  enforced  by  the  tendency  toward 
maximization  of  the  number  of  independent  enterprises,  though  it  eliminates  again 
the  profits  from  differentiation.  (2)  Differentiation  is  generally  contrary  to  the 
interests  of  nearby  consumers.  (3)  The  most  advantageous  differentiation  is  generally 
not  so  great  as  to  be  damaged  by  resale.  (4)  Uniform  f.  o.  b.  prices  would  be  more 
favorable  to  the  consumer  as  a  rule. 

2.  This  should  not  be  confused  with  the  irrelevant  technical  question  of  whether 
the  carrier  collects  the  freight  from  the  buyer  or  the  seller;  that  is,  whether  or  not 
it  appears  on  the  bill. 

3.  There  are  several  combinations  and  variations  of  this.  For  example,  the  creation 
of  zones  with  equal  prices  (A  +  F  or  A  -f  C)  or  calculation  of  the  freight  from  a 
fictitious  location  (basing-point  system) .  The  meaning  of  A,  F,  and  C  should  be  kept 
in  mind  in  what  follows. 

139 


140 


Part  Two.    Economic  Regions 


Let  do  in  Figure  40  be  the  individual  demand  with  regard  to 
the  delivered  price.  It  is  the  same  for  all  buyers,  whether  they  live 
close  to  or  far  from  the  factory,  since  it  relates  to  the  price  actually 
paid  by  each;  i.  e.,  to  the  local  price  prevailing  at  the  destination. 
The  demand  curve  of  a  customer  in  the  neighboring  place  with 
respect  to  the  f.  o.  b.  price  is  <ii.  This  demand  curve,  d^,,  lies  below 
the  demand  curve  do  by  the  vertical  distance  i,  which  is  the  unit 
freight  cost  from  the  factory  to  the  neighboring  place,  d^  is  valid 
only  for  all  customers  at  a  particular  distance  since  it  is  based  on 
the  factory  price,  which  represents  the  net  payment  to  the  manu- 
facturer and  which  varies  with  distance,  but  which  is  of  no  particular 


Amount 


Fig.  40.  Comparison  of  individual 
demand  with  respect  to  the  c.  i.  f. 
price  (do)  and  with  respect  to  the 
i.  o.  b.  price  (dj),  the  latter  as  seen 
by  a  buyer  in  a  neighboring  town. 
Vertical  distance  i  between  do  and 
dj:  unit  freight  from  factory  to 
neighboring  town. 


interest  to  the  purchaser.  We  assume  that  prices  have  already  been 
determined.  Let  a  vertical  line,  UT,  intersect  do  at  the  level  of  the 
uniform  c.  i.  f.  price.  It  will  cut  di  at  the  level  of  the  distant  f.  o,  b. 
price.  Let  a  horizontal  line,  HJ,  intersect  do  and  di  at  the  level  of 
the  uniform  f.  o.  b.  price.  The  corresponding  c.  i.  f.  price  then  lies 
on  do  vertically  above  the  intersection  with  d^.  A  straight  line,  KL, 
bisecting  UJ  for  reasons  to  be  given  later,  cuts  do  and  d^  at  the  level 
of  the  differentiated  f.  o.  b.  price  (policy  A) .  The  corresponding 
c.  i.  f.  price  lies  on  do  vertically  above  the  intersection  with  d^. 

From  this  it  follows  that  with  C  the  seller  pays  the  whole  freight, 
with  A  half  of  it,  and  with  F  no  freight  at  all.  As  as  consequence 
the  individual  market  under  C  is  everywhere  equally  large;  under 
F  it  declines,  independently  of  the  level  of  the  unit  price  in  the 
neighboring  place,  by  an  amount  proportional  to  the  freight.  The 
same  is  true  of  A,  except  that  the  amount  is  lost  is  always  half  as 
large  as  under  F. 


Some  New  Factors  ^4^ 

Geographic  differences  in  the  elasticity  of  demand  are  more 
difficult  to  determine.  The  elasticity  in  C7  is  ci  ==  UR  -^  QU;  in  E, 
e.  =  ES^  DE;  in  K  it  is  £3  =  KR^  QK;  in  /,  e,  =  JR-~  QJ.  Since 
QU  =  DE,  and  UR  >  ES,  ^  >  €2.   Corresponding  comparisons  give: 

Cl    >   €2    >   €3    >    €4 

In  words:  (1)  The  individual  demand  in  respect  to  the  c.  i.  £. 
price  is  more  elastic  than  the  individual  demand  as  a  function  of 
the  corresponding  £.  o.  b.  price  (ei  >  £2)  .*  This  is  true  of  every  price 
policy  for  one  and  the  same  place,  and  for  any  demand  curve;  not, 
like  the  following  propositions,  for  the  linear  only. 

(2)  If  f.  o.  b.  prices  for  increasingly  distant  places  differ  by  total 
freight  costs  (C) ,  (ei  >  €2)  falls;  '  if  they  differ  by  only  half  these 
costs  (A) ,  or  not  at  all   (F) ,  the  elasticity  of  the  demand  in  respect 

4.  The  reason  is  that  a  certain  percentage  change  in  the  f.  o.  b.  price  causes  a  smaller 
percentage  change  in  the  corresponding  c.  i.  f.  price,  whereas  the  absolute  change  is 
the  same  in  both  (see  E.  M.  Hoover,  "  Spatial  Price  Discrimination,"  Review  of 
Economic  Studies,  June,  1937,  p.  183,  note  1) .  Since  the  same  effect  is  produced  by 
a  smaller  percentage  change  in  the  c.  i.  f.  price,  the  elasticity  in  respect  to  it  is  greater. 

An  exactly  corresponding  situation  holds  when  a  market  center  is  surrounded  by  a 
supply  region— for  milk,  say.  The  same  change  of  price  in  the  town  affects  the  distant 
seller  more  strongly,  because  his  net  receipts  are  smaller  by  the  amount  of  the  freight 
costs.  Therefore  his  supply  in  respect  to  the  c.  i.  f.  price  is  more  elastic  than  in  respect 
to  the  f.  o.b.  price  (contrary  to  Hoover,  op.  cit.,  p.  191).  Besides  explaining  the 
profound  areal  effect  of  even  a  small  shrinkage  in  the  radius  of  the  supply  region,  it 
also  explains  why  agricultural  supply  reacts  so  strongly  on  world  market  prices,  particu- 
larly in  distant  overseas  countries,  and  within  these  countries  in  their  outlying  parts. 
Here  we  meet  a  further  difference  between  agriculture  and  industry.  In  the  former, 
supply,  in  the  latter,  demand,  is  especially  elastic  in  respect  to  the  c.  i.  f.  price.  Hence 
changes  in  demand  in  the  former,  in  supply  in  the  latter,  influence  the  c.  i.  f.  price 
relatively  little;  as,  conversely,  demand  in  the  former  (because  of  the  fixed  need  for 
food)  and  supply  in  the  latter  (because  of  fixed  costs)  react  less  upon  it.  Thus  price 
drops  should  exert  an  equilibrating  effect  in  agriculture  by  increasing  demand  less 
than  they  decrease  supply,  whereas  in  industry  they  should  decrease  supply  less  than 
they  increase  demand.  But  the  market  price  is  a  c.  i.  f.  price  in  agriculture  only;  in 
industry,  on  the  contrary,  it  is  an  f.  o.  b.  price.  Consequently  the  producer  pays  the 
freight  in  the  case  of  agriculture,  the  consumer  at  least  half  the  freight  in  the  case  of 
industry. 

In  regard  to  the  f.  o.  b.  price,  the  demand  of  the  customers  of  industry,  and  espe- 
cially of  mining,  is  also  less  elastic,  though  it  is  nevertheless  elastic  enough,  particularly 
at  the  boundaries  of  the  market  area  (except  under  C)  .  At  any  rate,  a  cyclical  decline 
in  demand,  especially  as  it  is  greater  here,  must,  depending  on  the  geographical 
elasticity  relationships,  lower  unregulated  market  prices  in  heavy  industry  and  mining 
more  than  the  market  prices  of  agricultural  goods.  Only  the  excess  supply  of  those 
overseas  marginal  farmers  who  are  really  bankrupt  but  generally  subsidized,  and  the 
reduction  of  supplies  by  industrial  combinations,  often  lower  agricultural  prices  more. 

5.  Except,  perhaps,  with  goods  that  are  not  strictly  comparable. 


1^2  Part  Two.     Economic  Regions 

to  current  f.  o.  b.  prices  increases  with  the  distance  (ea  >  csl  £2  >  u) , 
the  more  rapidly  the  smaller  the  difference  in  f.  o.  b.  prices  (€3  >  u)  -^ 
This  holds  true  for  a  comparison  between  different  places. 

(3)  In  respect  to  the  c.  i.  f.  price,  demand  becomes  continuously 
more  elastic  with  increasing  distance  from  the  production  site  than 
in  respect  to  the  corresponding  f.  o.  b.  price  (with  increasing  dis- 
tance from  the  factory  the  superiority  of  ci  over  e,  becomes  greater 
and  greater)  :  under  C,  because  the  elasticity  in  respect  to  the  cur- 
rent f.  o.  b.  price,  which  corresponds  to  the  constant  c.  i.  f.  price  (ca) , 
falls  absolutely  according  to  proposition  2;  under  F  and  A,  because 
the  elasticity  of  the  demand  in  respect  to  the  current  factory  price 
rises  with  distance,  though  less  than  in  respect  to  the  local  price. 
This  is  plausible  because  ci  >  £2  >  ^3  and  ti  >  £2  >  £4-^  Thus  €2 
increases  absolutely,  but  decreases  as  compared  to  ei.^ 

(4)  Elasticity  in  respect  to  the  c.  i.  f.  price  increases  with  it 
(fi  >  €3  >  £4)  in  all  places,  so  that  at  a  distance  even  small  changes 
in  the  local  price  may  elicit  a  greater  reaction  on  the  demand  under 
certain  circumstances  than  large  changes  in  the  vicinity  of  the  factory. 

(bb)  Preliminary  Study  (2)  :  Local  and  Spatial  Total  Demand— 
A  Comparisoji.  A  comparison  of  the  demand  at  the  location  of  a 
factory  alone  with  the  demand  throughout  its  whole  market  area  is 
but  a  comparison  between  individual  and  aggregate  demand.  The 
demand  of  n  fellow-townsmen  of  the  manufacturer  is  equal  to  n 
times  the  demand  of  any  one  of  them.  It  is  different,  except  with 
C,  when  these  n  buyers  are  distributed  over  the  entire  market  area. 
To  anticipate   the  result:    The   regional   demand   is  smaller,  and 

6.  Proof:  If  d^  is  continually  shifted  downward  it  will  intersect  UT  nearer  and 
nearer  to  its  (i.  e.,  UT'%)  lower  end,  and  HJ  nearer  and  nearer  to  its  (i.  e.,  HJ's) 
upper  end;  that  is  to  say,  in  the  former  case  demand  reacts  more  and  more  feebly  on 
the  rapidly  falling  factory  price,  and  in  the  latter  case  more  and  more  strongly  on  the 
factory  price  that  is  not  falling  at  all. 

7.  If  /  is  taken  as  any  arbitrary  c.  i.  f.  price  unconnected  with  E,  ei>e2>e4  can  be 
interpreted  also  as  follows:  With  the  same  sales  (associated  f.  o.  b.  and  c.  i.  f.  price) 
the  demand  in  respect  to  the  c.  i.  f.  price  is  (ei>e2) ;  on  the  contrary,  if  the  prices  are 
by  coincidence  equal,  it  is  more  elastic  at  the  same  place  in  respect  to  the  f.  o.  b.  price 

(f2>e4). 

8.  This  is  true  even  though  with  increasing  distance  the  same  change  in  the  factory 
price  causes  less  and  less  percentage  change  in  the  local  price.  Proof  for  F:  In  calcu- 
lating Ci  and  £2  the  denominator  is  the  same  {QU  =  DE) .  If  d^  is  shifted  downward, 
the  denominator  in  the  new  calculation  of  the  elasticity  decreases  in  both  cases  by  the 
same  absolute  amount.  But  only  with  ej  is  the  numerator  increased  by  the  same 
amount  (Fig.  45:  Cj  =  P2L  -i-  AP^,  62  =  p^K  -^  Bp„  [where  Bp^  =  Ap^].  New  calculations: 
£1  =  P^L  +  P7P2  -^  AP2  -  P.P^;  €2  =  pj  ^  Cp,  [where  pj  =  p^K  and  Cp,  =  AP^  -  P.P^]). 


Some  i^exu  Factors  i43 

generally  also  more  elastic,  than  the  local  demand.  In  both  cases, 
elasticity  increases  as  a  rule  with  price  and  distance. 

The  regional  demand  is  smaller:   If  there  are  n  persons  in  P 

(Fig.  21) ,  their  demand  (urban  demand)  will  be  rz  X  PQ,,  other 
things  being  equal.  But  if  the  same  persons  are  evenly  distributed 
over  an  area  with  the  radius  PF,  around  P,  the  demand  of  each  with 
price  policy  F,  and  generally  with  A  also,  will  be  smaller  than  PQ 

(rural  demand) .  If  the  straight-line  demand  curve  is  taken  once 
more  as  the  average  of  all  possible  shapes,  we  can  even  say  by  how 
much  the  rural  demand  falls  short  of  the  urban  demand:  It  amounts 
to  one  third  of  the  urban  demand.^  For  since  the  volume  of  a  cone 
equals  the  area  of  its  base  times  one  third  its  height,  the  demand 
at  any  one  point  in  the  circular  area  would  amount  on  the  average 
to  PQ/3,  and  at  n  points  to  rz  X  -PQ/3.  Now  we  see  why  the  metro- 
politan demand  (n  X  PQ)  is  so  much  more  attractive  to  industry 
than  the  rural  demand:  It  is  not  only,  and  not  always,  the  greater 
number  of  consumers  that  attracts,  but  also  the  demand  of  each, 
which  is  about  three  times  greater  in  the  limiting  case;  that  is,  when 
the  actual  sales  radius  is  equal  to  the  possible  one.  But  competition 
reduces  the  size  of  the  area  considerably,  and  it  is  precisely  the  boun- 
dary zones,  which  have  the  smallest  demand  of  all,  that  are  elimi- 
nated. In  the  remaining  area  the  individual  demand  is  still  smaller 
on  the  average  than  PQ,  but  generally,  and  above  all  with  A,  con- 
siderably larger  than  PQ/3.^° 

9.  If,  on  the  other  hand,  the  demand  curve  is  concave  upward,  the  demand  of 
country  dwellers  (compared  with  that  of  a  person  living  at  the  factory  site)  will  be 
less  than  one  third,  and  if  the  individual  demand  curve  is  convex,  more  than  one 
third,  of  what  would  correspond  to  their  numbers. 

10.  A  few  factors,  neglected  until  now,  modify  this  result.  Affluence,  or  at  any  rate 
population  density,  decrease  with  distance  from  a  town.  For  since  farmers  living  away 
from  the  city  pay  double  freight— in  the  manufactured  products  that  they  buy  and  the 
agricultural  products  that  they  sell— either  their  income  will  be  smaller  or  their  farms 
larger  than  in  the  vicinity  of  a  town.  But  even  with  the  same  income  and  at  the  same 
price,  especially  if  this  is  high,  the  individual  buys  fewer  and  fewer  urban  goods  with 
increasing  distance  from  the  town;  for  his  demand  depends  upon  price  relationships 
as  a  whole,  and  these  shift  more  and  more  in  favor  of  rural  products.  Consequently 
the  individual  demand  curve  is  rotated  more  and  more  toward  the  left  about  its 
intersection  with  the  »;-axis.  The  sales  cone  cannot  then  be  constructed  from  the 
individual  demand  curve,  but  must  be  constructed  from  a  special  one  that  falls  more 
abruptly  as  prices  increase.  Because  prosperity  and  the  desire  to  buy  decrease,  the 
rural  demand  throughout  the  entire  region  amounts  to  still  less  than  one-third  that  in 
the  town.  Only  the  decrease  in  population  density  counteracts  this:  More  farmers  with 
a  more  even  distribution  then  live  near  the  town,  where  their  demand  is  still  relatively 
large.  Since  for  all  three  reasons  demand  in  the  boundary  zones  is  particularly  small, 
their  elimination  raises  the  rural  demand  to  a  comparatively  high  degree,  though 
perhaps  absolutely  not  much  above  one  third  of  the  urban  demand. 


1^^  Part   Two.     Economic  Regions 

The  regional  demand  is  more  elastic.  Strictly  speaking,  this 
statement  holds  only  for  the  average  form  of  the  straight-line  demand 
curve;  but  it  is  therefore  valid  for  the  majority  of  conceivable,  if  not 
actual,  cases.  It  is  a  rule  of  thumb.  It  seems  plausible  because  a  rise 
in  price,  for  example,  diminishes  not  only  the  individual  demand 
(the  height  of  the  demand  cone),  but  also  the  number  of  buyers 
(the  radius  of  its  base).  Of  course  the  average  height  of  the  cone 
(which  is  the  relevant  magnitude  so  far  as  total  demand  is  concerned) 
is  decreased  by  less  than  its  maximum  height  (which  represents  the 
individual  demand  at  the  center  of  the  region)  .  It  is  therefore  neces- 
sary, at  least  for  the  average  case  in  which  the  demand  is  linear,  that 
rigorous  proof  of  the  statement  be  given.  It  is  offered  herewith  for 
the  case  where  the  market  region  is  restricted  by  nothing  but  trans- 
port costs.  In  this  case  curve  A  in  Figure  41  represents  the  total 
demand."  Now  let  d  be  the  individual  demand  at  the  site  of  produc- 
tion, D  the  total  demand  throughout  the  sales  region,  and  R  the  unit 
transport  costs,  borne  by  the  consumer,  from  the  production  site  to 
the  boundaries  of  the  region  (the  highest  freight)  at  the  factory  price 
p;  and  let  d\  D',  and  R'  be  corresponding  values  at  price  p'.  Then 
D-^D'  =  7ri?2rf/3  ^  ^i^'-'dys  =  R^d  -^  R'^d'  =  d' ^  d'\  since  with 
a  straight-line  demand  curve  R'  =  d'R  -^  d.  If  p  >  p',  ci  <  d'; 
d^d'  >  d'^  d'^;  d^d'  >  D-^D\  U  p  <  p'  then,  on  the  contrary, 
d^^  d^  <C  D  ^-  D\  That  is,  the  regional  demand  increases  with 
falling  prices  and  decreases  with  rising  prices  more  sharply  than  the 
individual  demand  at  the  factory  site;  in  short,  it  is  more  elastic  in 
respect  to  the  factory  price.^^ 

To  give  an  example:  with  a  linear  demand  D -^  D' =  d^ -^  d'^ 
=  R^  -^  R'^.  That  is,  the  regional  demands  at  various  factory  prices 
are  related  as  the  cubes  of  the  maximum  freights.  If,  for  instance, 
the  factory  price  is  raised  by  half  the  highest  freight,  the  regional 
demand  will  fall  to  1/8,  but  the  individual  demand  to  only  1/2. 
A  similar  proof  could  be  brought  for  the  case  in  which  the  market 

11.  The  following  symbols,  however,  do  not  refer  to  Figure  41. 

12.  In  still  more  general  terms:  The  smaller  the  necessary  area  the  weaker  is  the 
effect  of  a  price  change  on  the  total  demand.  When  the  area  becomes  a  point,  as  with 
a  town,  the  demand  is  therefore  least  elastic.  Consequently  outlying  demand  is  more 
elastic  than  local,  and  foreign  demand  more  elastic  than  domestic,  which  is  of 
importance  in  examining  the  transfer  problem.  It  is  interesting  to  understand  the 
other  side  of  the  situation  also.  The  lower  the  price,  the  more  does  a  change  in 
regional  size  affect  demand,  as  is  readily  seen  from  curves  A'  and  A  in  Figure  41.  But 
the  smaller  the  region  the  more  effective  is  its  change,  even  with  a  high  price.  In  the 
limiting  case,  point  concentration,  G  coincides  with  F,  and  the  effect  of  a  division  of 
the  town  among  several  producers  is  percentually  the  same  at  every  price. 


Some  New  Factors 


145 


area  is  restricted  by  competition    (A"  in  Figure  41  corresponds  to 
this) . 

As  for  the  relation  between  the  price  and  elasticity,  total  demand, 
exactly  like  individual  demand,  is  more  elastic  the  higher  the  price 
(always  assuming  a  linear  demand)  .    This  is  easily  seen  from  the 


0,  TO 

Individual  demand 


V      W  A      U 


Os  Oz 

Transport  funnel  Individual  demand  Total  demand 

Fig.  41.   Various  types  of  total  demand  curves 

OJJ      Volume  of  cone  resulting  from  revolution  of  O^FT  about  O^T  as  an  axis 

OV  Volume  of  truncated  cone  resulting  from  revolution  of  O^ADT  about  O^T  as 
an  axis 

OW  Volume  of  truncated  cone  resulting  from  revolution  of  O^RST  about  O^T  as 
an  axis 

OX  Volume  of  truncated  cone  resulting  from  revolution  of  OiPQT  about  O^T  as 
an  axis 

A  Greatest  possible  total  demand  as  a  function  of  factory  price 

A'  Demand  within  the  circumscribed  circle  p  {^M'P  =  O^A  =  EF)  as  a  function 
of  factory  price  ^^ 

A"  Total  demand  as  a  function  of  factory  price  when  price  and  distance  of  com- 
petitors are  given 

A'"  Total  demand  as  a  function  of  factory  price  when  price  at  areal  boundaries 
is  supposed  always  to  be  OP 

OM'  is  the  price,  p  the  size  of  the  area,  which  together  result  in  equilibrium.  The 
shipping  distance,  that  is,  the  circumference  beyond  which  no  more  demand 
is  supposed  to  come  to  O^,  does  not  reach  the  value  p  with  every  factory  price. 

equation  D  -^D'  =  R^  -^  R'^,  if  it  is  recalled  that  consecutive  equal 
absolute  (and  even  more  so  percentage)  price  increases  diminish 
R  successively  more  and  more.  So  much  for  the  elasticity  of  curve  A. 

13.  From  factory  price  OE  upward  this  restriction  in  regional  size  has  no  further 
influence  on  the  extent  of  the  total  demand.   Hence  A'  coincides  with  A  from  here  on. 


146  Part   Two.     Economic  Regions 

The  matter  is  exactly  the  same  if  the  radius  of  the  market  area 
cannot  be  greater  than  r  (or  p  in  equilibrium)  ,  regardless  of  what 
the  possible  shipping  distance  R  may  otherwise  be  (curve  A',  Fig.  41). 
We  let  R  increase  slowly;  that  is,  we  let  the  price  fall.  As  long  as 
R  <i  r,  the  given  boundaries  are  irrelelvant.  But  when  R  becomes 
greater  than  r,  an  increasingly  large  part  of  the  possible  demand 
will  not  be  realized  because  of  the  restriction  of  the  region;  i.  e.,  for 
this  reason,  too,  total  demand  will  become  less  elastic  the  lower  the 
price.^* 

If,  on  the  other  hand,  it  is  not  the  maximum  distance  of  the 
boundaries  of  a  producer's  market,  but  the  distance  and  the  prices 
of  competitors  that  remain  constant  (curve  A") ,  this  situation,  too, 
provides  an  additional  reason  why  elasticity  should  increase  with 
price.  In  Figure  41,  O.  is  the  location  of  Oi's  nearest  competition, 
which  limits  the  highest  f.  o.  b.  price  obtainable  by  O^  to  O^H;  that 
is,  to  the  equilibrium  price,  p,  and  the  corresponding  doubled 
shipping  distance  2p.  At  any  given  price,  OiB,  the  extent  of  sales 
obtainable,  BK,  is  equal  to  half  the  difference  between  the  actual 
and  the  highest  possible  price  {BK  =  BH  ~-  2)  .  Again  it  is  true 
that  an  equal  percentage  rise  in  price  shortens  the  sales  radius  per- 
centually  more  the  higher  the  price.  For  the  higher  the  price 
absolutely,  the  shorter  absolutely  is  the  sales  radius.  Now  since  this 
is  already  shorter  than  under  the  conditions  of  curve  A,  it  follows 
that  the  elasticity  of  curve  A"  increases  the  factory  price  even  more 
rapidly  than  that  of  A. 

Finally,  the  elasticity  of  demand  in  respect  to  distance  itself  is 
interesting;  that  is  to  say,  in  respect  to  transport  costs.  The  number 
of  persons  living  at  a  certain  distance  from  a  factory  (c27rr)  increases 
in  the  same  proportion  as  the  distance  (r)  .  The  elasticity  of  the 
individual  demand  in  respect  to  transport  costs,  on  the  contrary, 
rises  with  distance,  as  can  be  seen  from  Figure  40  if  one  thinks  of 
the  X-axis  as  passing  through  H  and  thus  obtains  the  elasticity  of  do 
in  respect  to  the  freight  drawn  into  the  figure  from  H  upward.  The 
elasticity  coefficient  of  the  total  demand  in  respect  to  distance  may, 
for  the  first  reason,  be  low  or  even  negative,  but  for  the  second  reason 
it  increases  with  distance. 

On  the  other  hand,  the  elasticity  of  the  total  demand  is  inde- 
pendent of  population  density,  since  this  influences  total  demand 
to  the  same  degree  at  all  price  levels. 

14.  One  may  say  also:  The  smaller  the  region  the  less  the  elasticity  of  the  total 
demand.  Yet  it  cannot  fall  below  the  elasticity  of  the  individual  demand,  but  only 
reach  it  in  the  limiting  case  if  the  whole  region  coincides  with  the  manufacturing  site. 


< 


Some  New  Factors  ^47 

(cc)  Geographical  Price  Discrimination.  With  price  discrimina- 
tion the  seller  asks  of  each  buyer  the  factory  price  that  will  yield 
the  highest  profit.  Where  it  does  not  involve  too  much  trouble, 
price  policy  A  is  therefore  the  best.  Now  how  is  the  most  favorable 
price  to  be  found  at  any  given  time? 

1.  The  Size  of  Price  Differences.  The  factory  price  of  an  isolated 
enterprise  influences  its  sales  and,  conversely,  marginal  revenue  does 
not  equal  price.  Hence  the  equilibrium  condition  also  does  not 
hold  in  its  limiting  form  (marginal  cost  =  price)  but  only  in  its 
general  form  (marginal  cost  =  marginal  revenue).  In  this  case  price 
discrimination  is  most  advantageous  when  this  condition  is  fulfilled 
for  each  single  buyer,  not  only  (as  with  F  and  C)  for  all  buyers 
together.^^  Marginal  revenue  depends  upon  the  strength  and  elas- 
ticity of  demand,  and  both  in  turn  depend  upon  distance.  Every- 
thing is  to  be  related  to  the  f.  o.  b.  price,  for  the  entrepreneur  is 
interested  only  in  the  effect  of  the  price  he  receives,  not  that  which 
the  buyer  pays. 

Now  let 

t  =  freight  per  unit  from  factory  to  buyer 
P  =  delivered  price  \P  =  f  {n)  ] 
p  =  factory  price   {p  =  P  —  t) 
n  =  individual  demand  at  delivered  price 
e  =  elasticity  of  demand  in  respect  to  delivered  price 
P  X  dn    .         percentage  change  in  quantity 
n  X  dP'    '     '    percentage  change  in  price 

c  =  marginal  costs. 

Then  marginal  revenue  is: 

d(Pn)      ^_Pxdn  +  nXdP      ^_^      P      ^ 
dn  dn  e 

Marginal  revenue  equals  marginal  costs  when  P  —  t  —  (P  -^  e)  =  c. 
Hence  it  follows  that  the  most  profitable  factory  price  is  p  =  c 
+  (P-^e),  or  p  =  c  —  nf\n);  or,  more  correctly,  since  no  quantities 
containing  p  remain  on  the  right  side  of  the  equation,^" 

15.  Only  in   the  case  of  a  prescribed  market  area   is   the  marginal  condition  not 
necessarily  fulfilled  at  the  point  of  greatest  profit.   See  Losch,  "  Geographic  der  Preise  " 

(in  preparation) .   On  the  contrary,  total  revenue  >  total  costs  must  always  be  a  second 
condition. 

16.  The  derivation  is  E.  M.  Hoover's    ("  Spatial  Price  Discrimination,"   Review  of 
Economic  Studies,  June,  1937,  pp.  182-191)  . 


1^8  Part  Tiuo.    Economic  Regions 


Obviously  the  factory  price  is  not  the  same  for  all  buyers,  but 
depends  upon  t,  c,  and  c.  We  shall  now  discuss  the  influence  of 
these  three  factors  on  p,  using  the  simple  first  formulation 

[p  =  C+{P^e)]. 

Distance}^''  The  greater  the  distance  of  the  customer  from  the 
factory,  the  greater,  ceteris  paribus,  is  the  factory  price  which  he  has 
to  pay.  p  increases  with  t  when  e  and  c  are  constant.  £  does  not 
remain  constant  as  a  rule,  but  increases  with  distance  exactly  as  t. 
(See  the  preceding  section  on  this  point.)  While  p  rises  with 
increasing  t,  it  falls  with  increasing  e.  Whether  p  rises  and  falls 
with  distance  therefore  depends  on  the  relation  between  e  and  t. 

What  are  the  conditions  under  which  p  will  rise  with  distance? 
Let  ^1  be  nearer  the  factory  than  An.  p^  will  then  be  greater  than 
pi  if 

i-C  +   ^2    >^    gig  +   ^1 
€2  1  €i  1 

From  this  it  follows  that 

€2(^1  +  <^)  +  (^2  -  ^1)       J 
^1(^2  +  c)  ^ 

But  —^ — r-^  is  necessarily  smaller  than  1.    The  remainder  of  the 

€1(^2  +  c) 
inequality  will  be  less  than  one  if  (co^i  +£2^)  <  (ei^i  +  €ic).  But  e.c 
is,  as  a  rule,  greater  than  eiC.  If  the  inequality  is  to  hold,  t  would 
have  to  show  a  greater  percentage  increase  than  e.  But  this  is  highly 
improbable,  since  e  can  become  infinite  while  t  always  remains 
finite.  If  in  the  absence  of  better  information  we  assume  a  straight- 
line  demand  curve  as  the  average  shape,  e  will  increase  more  rapidly 
than  t.  That  is,  the  very  shape  of  the  demand  curve  makes  it  unlikely 
that  p  will  increase  with  t.  But,  in  addition,  even  in  the  few  cases 
in  which  p  might  increase  with  t  as  far  as  demand  is  concerned, 
it  can  actually  happen  only  in  the  still  fewer  cases  where  A^  can  be 
prevented  from  buying  through  A-^  rather  than  directly  from  the 
factory.  It  follows  that  the  factory  price  will  fall  with  distance  as  a 
rule.'^''^^'''^ 

16a.  The  subsections   "  Distance,"   "  Elasticity,"   and   "  Marginal   Cost "   have   been 
translated  from  the  fuller  version  of  the  first  German  edition,  pp.  96-98. 

17.  This  is  shown  in  Figure  42  as  follows:  If  p  and  e  are  variables  but  c  is  held 

constant,   then  p' = is  a  rectangular  hyperbola  which,  for  e  >  1,  lies  entirely 

e—  1 


Some  N<?zv  Factors 


149 


Elasticity.  The  more  elastic  the  demand  the  lower  is  the  I'actory 
price  that  must  be  paid.  This  statement  is  absolutely  valid  for 
constant  t,  and  usually  holds  also  for  t  =  /(«).  If  demand  is  very 
elastic,  the  factory  price  virtually  coincides  with  marginal  cost:  the 
hyperbola  p'  =  0(e)  approaches  its  asymptote  p  =  c.  The  price  can- 
not fall  below  marginal  cost.  Yet  if  e  <  1  this  would  have  to  be  the 
case.  It  follows  that  the  equilibrium  point  must  lie  on  the  elastic 
stretch  of  the  demand  curve. ^° 


within    the    first    quadrant 
t 


P" 


Its    asymptotes    are    p^c   and    e  =  l.      Since    t  =  f  (e)  , 
represents  a  family  of  similar  hyperbolas  with  the  asymptotes  p  =  0  and 


e  =  1.  Finally,  p  =  p'  -\-p".  For  e  >  1,  p'  falls  with  increasing  c.  Consequently  p" 
must  rise  at  least  as  much  as  p'  falls,  if  p  is  to  increase  with  e.  But  p"  can  increase 
with  increasing  e  only  if  even  small  increments  in  e  raise  the  corresponding  hyperbola 
greatly,  that  is,  if  t  increases  very  rapidly.  Figure  42  shows  furthermore  that  with 
constant  e  the  factory  price  will  increase  less  with  distance  the  greater  is  e.  For  e  >  2 
the  factory  price  increases  by  less  than  the  freight.  This  follows  from  Figure  42  and 
from  the  equation 


1 


-  1 


which  is  fulfilled  for  e  =  2. 


Fig.  42. 

18.  Since  the  excess  profits  of  the  nearer  entrepreneur  are  greater,  therefore,  than 
those  of  the  more  distant  ones,  the  former  have  a  greater  influence  on  the  choice  of 
location  than  would  correspond  to  their  demand,  to  say  nothing  of  their  numbers— 
a  further  reason  for  the  concentration  of  industry  in  large  cities. 

19.  This  is  not  only  rational  but  also  realistic.  One  need  think  only  of  the  many 
instances  in  which  a  product  has  a  uniform  price,  or  in  which  the  seller  pays  at  least 
part  of  the  freight. 

20.  The  left  branch  of  the  hyperbola  p'  =  <p  (e)  is  limited  by  p  =  c  in  the  upward 
direction  and  by  e  =  1  toward  the  right,  and  it  always  goes  through  the  origin.  With 
a  negative  elasticity  the  price  is  thus  positive,  but  it  is  too  low.  For  0  <  e  <  I,  the 
price  becomes  a  subsidy  payment.  This  would  make  marginal  revenue,  which  for 
0  <  e  <  1  is  negative,  positive  again.  As  production  increases,  total  costs  rise  and 
subsidy  payments  fall.  Hypothetically  speaking,  production  is  expanded  in  this  case 
until  marginal  cost  equals  the  marginal  savings  in  subsidy  payments.    For  e  <  1   the 


i-o  Part  Tu'o.     Economic  Regions 

Marginal  Cost.  The  higher  the  marginal  cost  the  higher  is  the 
factory  price  which  the  same  buyer  must  pay.  How  does  a  change 
in  c  affect  the  spatial  price  dispersion,  i.  e.,  the  dispersion  of  the 
factory  prices  which  are  established  for  different  distances?  Since  p' 
changes  proportionately  with  c,  while  p"  is  independent  of  c,  a 
change  in  c  affects  p  ==  p'  -\-  p"  more  the  greater  p'/p''  is.  Since  this 
fraction  increases  with  distance,  an  increase  in  marginal  cost  raises 
the  factory  price  for  distant  buyers  more  than  for  near-by  customers. 
Thus  an  increase  in  marginal  cost  reduces  spatial  price  differences 
and  a  decrease  widens  them.-^  As  the  reduction  in  the  market  area 
that  is  made  possible  by  price  differentiation  raises  cost,  and  thus 
diminishes  spatial  price  differences,  it  brakes  itself. 

Example:  We  now  apply  the  results  to  the  characteristic  case  in 
which  the  individual  demand  is  linear,  and  offer  first  an  algebraic 
solution.  From  the  demand  equation,  p  -\-  t  =  —  [{b/a)n'\  +  h,^^  it 
follows  that  e=  {p  -\-  t)  -i-  {b  —  p  —  t)  and  hence,  according  to  the 
formula  for  the  factor  price  p  =  ^{b  -\-  c  —  t).  Since  b  and  c  are  given, 
p  falls  as  t  rises.  For  two  different  places  we  get  pi  —  p2  =  ^{t2  —  ti). 
Thus  with  a  linear  demand  schedule  the  factory  price  falls  with 
distance,  and  by  half  the  freight. 

As  for  the  geometrical  solution,  do  to  dz  in  Figure  43  are 
individual  demand  curves  in  respect  to  the  f.  o.  b.  price  in  three 
places.  Bo  to  Bo,  separated  successively  from  one  another  by  the 
distance  i.  Bo  is  the  site  of  the  factory.  The  marginal  revenue,  Uo', 
is  easily  derived  from  the  demand  curve  do  by  drawing  the  line  AN' 
in  such  a  way  that  N'  bisects  ON.~^  The  curve  for  marginal  revenue 


equality  of  marginal  revenue  and  marginal  cost  means  minimization  of  losses  rather 
than  maximization  of  profits.  The  equality  of  marginal  cost  and  marginal  revenue 
is  therefore  only  one  equilibrium  condition;  the  other  is  that  there  must  be  a  true 
profit  maximum. 

21.  I  doubt  that  the  intensification  of  spatial  price  differences  that  has  been 
repeatedly  noticed  during  a  depression  requires  an  explanation  as  complicated  as  that 
given  above,  or  even  admits  of  it.  A  general  reduction  in  costs  acts  differently  from  a 
partial  decrease,  for  which  alone  our  analysis  is  valid.  H.  W.  Singer  ("A  Note  on 
Spatial  Price  Discrimination,"  Review  of  Economic  Studies,  October,  1937,  p.  77) ,  who 
attempted  such  an  explanation,  based  his  argument  solely  on  the  improbable  case  that 
6  is  constant. 

22.  Where  p,  t,  and  n  have  the  meaning  given  above,  and  b/a  and  b  are  the  para- 
meters of  the  particular  straight-line  demand  curve.— W.  F.  S. 

23.  Proof:   General  equation  for  the  linear  demand  curve:  y  =  —  _x  -(-  6;  for  the 

b  "" 

total  revenue  curve,  i2  =  (— _x  +  b)x;  whence  by  differentiation  is  derived  the  mar- 

h  ^ 

ginal  curve,  R'  =  —2-x  -f-  b.    (For  a  geometric  proof,  see  J.  Robinson,  The  Theory  of 

a 
Imperfect  Competition  [London,  1934],  p.  32-W.  F.  S.) 


Some  New  Factors 


151 


Amount 


Fig.  43.  (a)  Three  individual  demand  curves 
with  respect  to  f.  o.  b.  price  as  function  of  dis- 
tance from  site  of  factory,  (b)  Corresponding 
total  revenue  curves,  (c)  Corresponding  trans- 
port cones. 


j_2  Part  Two.    Economic  Regions 

as  a  function  of  total  sales,  £/',  is  derived  from  the  individual  mar- 
ginal receipts  by  horizontal  addition.  This  intersects  the  marginal 
cost  curve,  K\  at  G.  Here  marginal  costs  equal  marginal  revenue; 
hence  it  is  the  point  of  highest  profit.  The  points  of  intersection 
of  HG  with  the  individual  marginal  revenue  curves  give  the 
optimum  amounts  that  will  be  shipped  to  each  place.  The  factory 
prices,  po,  pi,  and  p2  (which,  incidentally,  all  lie  on  the  straight 
line  HPo)  can  be  read  off  from  the  corresponding  demand  curves. 
Finally,  the  corresponding  delivered  prices,  Po,  Pi,  and  P2,  lie  on  do- 

It  is  easily  seen  that  these  prices  differ  by  f/2.  According  to  a 
well-known  theorem  P^L,  for  example,  is  equal  to  AH -^2  and 
p^K  =  CH  ^  2.  Since  AH-CH  =  i,  P^L  =  p^K  +  f/2,  and  so  on. 
Furthermore,  it  is  clear  that  for  every  place  the  price  lies  halfway 
between  the  variable  direct  costs  and  that  price  at  which  nothing 
more  would  be  sold;  that  is,  where  the  elasticity  of  the  gross 
profit  in  respect  to  the  amount  sold  is  equal  to  1  (for  example, 
yp_^  -^  p^C  =  I) .  If  one  were  to  try  to  dispose  of  a  larger  or  smaller 
amount,  the  gross  profit  from  the  buyers  concerned  (that  is,  receipts 
less  variable  costs)   would  be  smaller  in  both  cases   (Fig.  43b)  .^*'"^ 

All  this  is  made  especially  clear  by  the  traffic  funnel  in  Figure 
43c,  where  the  symbols  are  the  same  as  for  the  corresponding  lines  in 
Figure  43a.  D'L  is  marginal  costs,  assumed  to  be  constant  for  the  sake 
of  simplicity;  LPq  is  the  monopoly  profit  from  home  buyers,  and  PqA 
the  line  of  c.  i.  f.  prices.  ALX  would  be  a  cross  section  of  the  traffic 
funnel  if  no  monopoly  profit  were  taken  but  a  uniform  factory  price 
at  the  level  of  the  variable  costs  were  asked.  APqX  is  the  funnel 
with  monopolistic  prices.  If  one  unit  were  sold  at  every  point  on 
the  line  OD'r^  the  area  OWLD'  would  represent  variable  production 
costs,  the  triangle  WAL  transport  costs,  and  the  triangle  LAPq  the 
gross  monopoly  profit  without  deduction  of  fixed  costs.  Or,  from  a 
different  standpoint,  the  quadrilateral  area  WAPqL  is  the  amount 
paid  by  buyers  over  and  above  the  variable  costs  of  production.  One 
third  of  it  goes  for  freight  paid  by  the  buyers  themselves,  one  third 
for  freight  paid  by  the  shipper,  and  one  third  for  monopoly  profit. 

24.  Construction  of  the  curves  for  gross  profits  assumes  that  the  single  buyer  exerts 
no  influence  on  marginal  costs. 

25.  A  similar  but  somewhat  simpler  diagram  is  given  by  J.  Robinson,  op.  cit.,  p.  183. 
Mrs.  Robinson  treats  also  a  simple  case  of  curvilinear  demand  curve.— W.  F.  S. 

26.  The  sales  radius,  which  would  be  represented  in  the  demand  cone  by  the  highest 
possible  freight,  may  be  shown  in  this  so-called  traffic  funnel  also  by  the  greatest 
amount  sold  per  buyer— the  line  OD'. 


Some  New  Factors  153 

The  three  triangles  of  equal  area  into  which  the  quadrilateral  is 
divided  correspond  to  these  amounts. ^^ 

Now  of  course  the  same  amount  will  not  be  sold  at  every  point 
on  a  radius  of  the  market  area,  even  when  it  is  assumed  that  the 
buyers  are  evenly  distributed.  On  the  contrary,  the  sales,  d,  per 
buyer  fall  from  OD'  to  zero  with  the  distance  from  D'.  On  the 
other  hand,  the  number,  n27rt,  of  buyers  (n  per  freight  unit)  at  a 
certain  distance  (measured  in  transport  costs,  t)  increases  propor- 
tionately with  distance.  From  this  foUoAvs  the  equation  for  total 
sales  at  a  certain  distance:  Dt  =  d  X  riZ-irt.    With  a  linear  demand 

t  ^  —-d  4-  h.    Therefore  D*  = d'^  +  nZTchd.    This  is  a  para- 

a  a  ^ 

bola,  with  its  vertex  at  the  point  {a  ^-  ^/abirn  -=r-  2)  as  drawn,  with 
the  ordinates  shortened,  in  Figure  43c.  It  follows  that  if  R  is  the 
radius  of  the  market  area,  the  combined  demand  of  all  the  con- 

sumers  at  the  distance  -^  will  generally  be  of  the  greatest  importance, 

whereas  the  total  demand  of  nearer  and  more  distant  consumers 
will  decrease  symmetrically.^^  Consequently  the  monopoly  profit, 
YPm  =  LPo  -^  2,  is  at  the  same  time  the  average  profit  per  unit,  and 
the  total  monopoly  profit  is  equal  to  this  quantity— no  longer  mul- 
tiplied by  WL,  however  (and  thus  no  longer  equal  to  the  triangle 
A  LPo) ,  but  multiplied  by  the  content  of  the  area  enclosed  by  the 
parabola  Dt  and  the  line  OD\  It  is  assumed  here  that  the  market 
area  is  not  encroached  upon  from  without. 

2.  The  Limits  of  Discrimination.  Besides  the  normal  shape  of 
the  demand  curve  there  is  still  another  reason  why  the  price  at  the 
factory  is  rarely  higher  for  distant  buyers  (A  2)  than  for  those  near 
by    (^1)  :  otherwise  it  would  be  advantageous  for  A  2  to  purchase 

27.  The  profit  triangle  is  LAPg.  Thus  profits  decrease  with  distance  exactly  as  do 
agricultural  rents.  However,  the  farmer  gets  the  same  rent  on  each  unit,  which  there- 
fore differs  only  among  different  farmers,  whereas  the  profit  of  the  industrialist  varies 
with  the  location  of  the  buyer. 

28.  It  is  now  clear  why  competition  is  so  keen  at  their  boundaries  when  market 
areas  are  reduced  by  competition:  most  of  the  demand  of  factories  which  themselves 
are  located  in  small  places  is  here.  If  areas  are  curtailed  but  little,  here  is  one  of  the 
reasons  why  foreign  trade  also  decreases  with  distance.  In  Germany,  powdered  and 
broken  pumice  has  a  market  area  limited  only  by  freight,  and  linoleum  a  market  area 
that  is  limited  in  certain  directions  only  by  freight;  because  all  the  former  is  produced 
in  one  single  district  and  the  latter  made  chiefly  in  but  a  few  factories.  In  1938  the 
most  frequent  shipping  distance  by  rail  was  about  300  to  375  miles  for  the  former 
and  about  375  to  430  miles  for  the  latter,  or,  in  accordance  with  theory,  almost 
exactly  half  the  maximum   (about  750  and  800  miles  respectively)  . 


154 


Part  Two.     Economic  Regions 


througli  A-i_.^^  Conversely,  the  factory  price  for  A^  can  exceed  that 
for  A2  only  by  the  freight,  /,  from  A 2  to  A^  at  the  most;  else  A-, 
would  order  through  A2.  As  for  the  c.  i.  f.  price.  Pi  can  be  above 
or  below  Po  by  /  at  the  most,  and  similarly  the  extent  of  fluctuation 
for  P2,  when  Pi  is  given,  is  equal  to  twice  the  freight  between  the 
two  places;  whereas  the  difference  between  Pi  and  P2  can  be  equal 
to  the  single  freight  at  the  highest. 


Amount 


Fig.  44.   Geometric  solution  of  limits  of  price  differentiation 

How  must  the  demand  be  constituted  in  order  that  factory  prices, 
differentiated  irrespective  of  the  possibility  of  intermediate  trade, 
shall  never  differ  by  more  than  the  freight?  We  shall  discuss  this 
question  only  briefly  because  it  is  rather  difficult,  and  because  it  is 
important  only  for  those  demand  curves  that  differ  widely  from  the 
average,  as  will  be  seen  later. 

Geometrical  Solution:  Let  ^0  in  Figure  44  be  the  marginal  costs 
without  freight  at  the  factory  site  Bq-,  (ki  =  ^0  +  i)  the  marginal 
costs  including  freight  for  delivery  to  the  place  Bj;  [kz  =  ^0  +  2z) 
for  delivery  to  B2,  twice  as  far  away;  and  so  on.  For  purchasers  at 
5o  let  OPo  be  the  price  that  yields  the  highest  profit,  and  P^Ao  the 
amount  sold  to  each  buyer  at  this  price. 


29.  It  must  be  remembered,  however,  that  interrupted  hauls  are  more  expensive 
than  direct  hauls. 


Some  New  Factors  155 

First:  How  must  the  individual  demand  curve  d  look  in  order 
that  the  factory  price  shall  be  the  same  for  all  buyers  wherever 
they  may  be,  despite  the  tendency  to  discrimination?  So  far  we 
know  only  one  point  on  d:  Aq.  We  draw  through  A^  the  rectangular 
hyperbola  h-^,  whose  asymptotes  are  the  };-axis  and  the  horizontal 
y  =  Kq.  As  the  product  x  {y  —  ko) ,  which  represents  profit,  is  the 
same  for  every  point  on  this  hyperbola,  d  must  touch  the  hyperbola 
at  Ao,  and  otherwise  lie  to  the  left  of  it.  Else  OP  would  not  be  the 
most  advantageous  factory  price  for  a  buyer  at  Bq.  Next  we  draw 
through  Ao  the  rectangular  hyperbola  /?/,  whose  asymptotes  are 
X  =  0  and  y  =  k^.  If  d  and  /z/  touch  at  Aq  and  if  d  lies  otherwise 
to  the  lejt  of  /z/,  a  greater  profit  cannot  be  obtained  at  B^  with  any 
other  delivered  price  than  OPq.  The  factory  price  for  B^  is,  there- 
fore, lower  by  /  than  that  for  Bq.  The  condition  that  would  have  to  be 
fulfilled  if  the  delivered  price  in  Bi  is  to  lie  above  OPq  is  that  d  must 
pass  above  Aq  and  to  the  right  of  /?/.  Hence  not  /z/,  but  a  hyperbola 
with  the  same  asymptotes  and  lying  to  the  right  of  it,  would  touch 
d.  If  the  point  of  tangency  were  between  y  ^  ks  and  y  =  ki,  it 
would  be  advantageous  in  shipping  to  B^  for  the  entrepreneur  at  Bo 
to  absorb  part  of  the  freight.  The  condition  under  which  B^  would 
pay  all  the  freight  is  that  the  point  of  tangency  must  lie  on  the  line 
A/Ai.  The  nearer  it  is  to  /ii  the  greater  is  the  profit  from  buyer  ^5^. 
Thus,  between  y  ^  k^  and  y  =  k^,  d  must  lie  within  the  vertically 
hatched  area,  and  in  such  a  way  that  no  hyperbola  of  the  group 
defined  by  the  asymptotes  x  =  0  and  y  =  k^  touches  it  anywhere 
else  than  at  y  =  ki.  Similarly  two  hyperbolas  can  be  drawn  through 
A  I,  of  which  the  steeper,  ho  (asymptotes  x  =  0,  y  =  ki) ,  limits  the 
farther  course  of  d  toward  the  right.  The  flatter  one  is  superfluous, 
since  the  left  limit  for  d  is  given  by  the  flatter  of  the  hyperbolas 
passing  through  /i/  (asymptotes  x  =0,  y  ==  kz) .  If  the  construction 
is  carried  further  a  cornucopia-shaped  area,  vertically  hatched  in 
Figure  44,  is  obtained,  within  which  d  must  lie  if  the  factory  price 
is  to  be  independent  of  distance. =*°  To  this  is  added,  as  a  second 
condition,  that  d  must  lie  within  this  area  in  such  a  way  that  the 
ordinates  of  the  points  of  tangency  of  the  profit  hyperbolas  must 
differ  by  exactly  the  freight. 

Second:  If  the  factory  price  is  to  rise  with  distance,  the  cornu- 
copia must  be  more  steeply  inclined  above  A-^'A^^,  as  can  readily  be 
seen.    Then  h-^  and  /?/  still  constitute  the  extreme  limits  above  /4/ 

30.  All  demand  curves  that  rise  above  the  upper  limits  {Ao,  A^,  A^,  and  so  on)  lead 
to  greater,  and  all  that  fall  beneath  the  lower  limits  {Ao,  A^',  A^ ,  ■  ■  •)  lead  to  smaller, 
price  differences  than  would  correspond  to  the  freight  differences. 


jr6  Part  Two.    Economic  Regions 

and  Ai,  and  they  are  steeper  than  /zz  and  hz.  In  this  case,  therefore, 
the  elasticity  of  the  demand  in  respect  to  the  delivered  price  must 
fall  with  distance  more  slowly,  if  at  all,  than  in  the  preceding  case. 
This  we  have  already  seen  on  page  149. 

Third:  If  the  factory  price  is  to  fall  with  the  distance  of  buyers, 
the  cornucopia,  and  with  it  the  demand  curve,  obviously  must  be 
less  steeply  inclined.  This  means  that  with  a  rising  price  the  elas- 
ticity of  the  demand  is  increased  relatively  quickly.  A  subcase 
deserves  special  attention.  Suppose  that  the  group  of  hyperbolas 
determined  by  the  asymptotes  x  =  0  and  y  =  k^  touched  the  demand 
curve  halfway  between  y  =  k^  and  y  =  k^.  This  would  mean  that 
the  delivered  price  would  rise  with  increasing  distance  by  only  half 
the  freight,  and  that  the  price  at  the  factory  would  therefore  fall 
by  the  same  amount.  It  could  easily  be  shown  ^^  that  the  limits  of 
the  cornucopias  in  this  case  would  be  straight  lines,^^  the  steeper 
one  of  which  would  have  the  equation 

whereas  the  equation  for  the  flatter  one  would  be 


\     Xo      / 


4- 2yo-f 


where  Xo  =  Po^o  and  yo^KoPo.  The  scope  of  d  is  horizontally 
hatched  in  Figure  44.  In  this  case  among  others  the  demand  curve 
itself  can  be  a  straight  line.  Conversely,  it  is  true  that  when  the 
demand  curve  is  a  straight  line  the  entrepreneur  always  pays  half 
the  freight.^^ 

Algebraic  solution:  From  the  formula  for  the  factory  price  there 
follows  as  the  c,  i.  f.  price  for  B^, 

p  gjC  -f-  ^iti 

ei  — ■  1 

and  for  Bz, 

eoC  +   £2^2 

31.  The  proof  is  omitted  in  order  not  to  overburden  the  text  with  mathematics. 

32.  This  is  strictly  true  only  when  /  is  very  small.  Otherwise  at  least  the  points  of 
intersection  of  the  branches  of  the  hyperbolas  lie  on  a  straight  line. 

33.  Strictly  speaking,  he  does  not  pay  half  the  freight,  which  represents  variable  costs 
that  the  buyer  must  make  good  in  any  case,  but  he  foregoes  profit  or  compensation  for 
his  fixed  costs  to  the  extent  of  half  the  freight. 


Some  New  Factors  *57 

Let  Bo  be  farther  away  from  the  factory  than  B^.  If  P2  is  higher,- 
the  condition  under  which  the  delivered  price  will  not  differ  by 
more  than  the  freight  is  P2  —  -Pi  ^  ^2—^1;  or,  if  ^2  —  ^1  =  h 

e,  {c  +  h  +  i)  ^  £2  {c  +  ^2)  +  i 

It  will  be  found  that,  among  others,  the  elasticities  resulting  from  a 
straiofht-line  demand  curve  fulfill  this  condition. 

3.  Application  {Dumping,  Overlapping  Areas,  Basing  Point) . 
Dumping,  or  factory  price  discrimination  in  favor  of  more  distant 
buyers,  need  not  by  any  means  imply  invasion  of  an  outside  market. 
There  exists  rather  a  desirable  form  of  dumping  in  the  more  remote 
part  of  an  undisputed  home  market,  as  we  have  shown. 

An  overlapping  of  areas  in  the  case  of  homogeneous  products, 
that  is,  dumping  in  the  market  area  of  a  competitor,  on  the  other 
hand,  is  often  a  sign  of  disintegration  or  panic,  or  a  result  of  megalo- 
mania, and  to  this  extent  concerns  more  the  psychiatrist  than  the 
economist.  At  the  least  it  is  an  outcome  of  a  thoughtless  disregard 
of  distance.^*  In  America  especially  there  have  been  many  com- 
plaints about  such  cross-hauling.  The  Federal  Trade  Commission 
has  calculated  that  in  1928-29  it  caused  unnecessary  freight  in  the 
cement  industry,  for  example,  amounting  to  some  20  per  cent  of 
the  total  production  and  marketing  costs. ^^  Exact  analysis  shows, 
however,  that  quality  differences  are  often  involved;  or  that  where 
statistics  are  broken  down  according  to  large  areas  of  localities  we 
are  dealing  with  only  apparent  cross-hauling,  and  in  reality  with 
"  small  boundary  trade."  The  cross-hauling  proper  that  remains  is 
often  quantitatively  negligible.  It  has  been  said  in  justification  of 
cross-hauling  that  it  is  necessary  in  industries  with  high  fixed  costs 

34.  Perhaps  because  a  producer  is  not  sure  of  his  costs,  is  not  acquainted  with 
neighboring  buyers  or  shippers,  wishes  to  continue  accidental  business  relations,  enjoys 
exceptional  freight  rates  that  are  much  too  low,  or  in  transactions  within  the  concern 
does  not  worry  over  distances.  A  certain  amount  of  cross-hauling  could,  however,  be 
avoided  only  if  production  were  more  mobile.  Such  unavoidable  cross-hauling  would 
occur  when  the  sites  of  those  producers  or  consumers  chiefly  concerned  cannot  handle 
a  sudden  falling  off  in  production,  or  sudden  great  demands  such  as  the  threat  of  a 
bad  harvest  or  extensive  construction.  Fundamentally,  market  areas  shift  temporarily, 
and  under  certain  conditions  a  market  area  may  even  become  a  supply  area.  This  may 
lead,  as  a  precaution,  even  to  normal  orders  going  in  part  to  distant  shipper  in  order 
to  be  sure  of  them  in  case  of  peak  demand.  All  this  is  confirmed  by  the  findings  of 
the  Baustoffleitstelle  and  the  Dienststelle   (formery  Biiro)   fiir  Transportordnung. 

35.  T.  K.  Urdahl  and  L.  J.  O'Neill,  "  Operation  of  the  Basing  Point  Provisions  in 
the  Lime  Industry  Code,"  NRA,  Division  of  Review,  Work  Materials  No.  65,  1936, 
pp.  75  f. 


1^8  Part  Two.     Economic  Regions 

in  order  to  assure  an  adequate  volume  of  business,^^  and  even  that 
with  falling  marginal  costs  it  may  lead  to  a  drop  in  domestic  prices.^^ 

But  these  arguments  overlook  the  fact  that,  especially  within  the 
same  country,  reciprocal  dumping  inevitably  develops  from  uni- 
lateral dumping,  and  that  none  of  the  participants  therefore  receives 
additional  orders,  though  all  incur  additional  expenses.  That  dump- 
ing should  be  answered  by  dumping  is  only  psychologically,  not 
economically,  necessary.  It  would  be  more  advantageous  to  employ 
a  part  of  the  freight  costs  that  dumping  must  absorb  to  prevent 
foreign  dumping  into  the  home  market,  instead  of  invading  another 
market.^^ 

As  unlimited  dumping  leads  only  to  pressure  on  prices  and  all- 
round  losses,  the  basing-point  system  attempts  to  replace  it  with 
regulated,  or  limited,  dumping.  The  simplest  of  its  many  forms  is 
that  in  which  all  factory  prices  are  the  same  and  the  freight  from 
the  basing  point  to  the  buyer  is  added  to  all.  Producers  outside  the 
basing  point  therefore  charge  their  customers  more  or  less  than  the 
actual  freight,  according  to  circumstances.  Only  thus  in  the  limiting 
case  can  all  producers  compete  at  the  same  price  for  every  buyer 
(quality  rather  than  price  competition) .  They  will  not  do  so  in 
reality,  of  course,  if,  in  the  case  of  unfavorably  located  customers, 
they  had  to  absorb  more  freight  than  would  correspond  to  the  profits 
from  near-by  customers  plus  the  share  in  the  fixed  costs  (m) .  In 
addition,  the  permissible  freight  absorption  will  sometimes  be  still 
further  limited  by  agreement.  If  the  same  factory  price  is  to  hold 
for  all  customers  wherever  situated,  the  freight  at  most  from  factory 
to  basing  point  can  be  absorbed  [h) .  In  other  agreements,  the 
absorbable  freight  will  be  fixed  at  a  percentage  of  the  factory  price 
(z)  .^^  In  any  case,  the  maximum  degree  of  permissible  dumping 
with  the  basing-point  system  is  automatically  established  for  every 
place  in  the  area  of  a  competitor;  and,  except  at  the  geographical 
boundaries  of  any  area  that  can  be  won  at  all  by  dumping,*"  it  will 

36.  G.  Seidler,  "  The  Control  of  Geographic  Price  Relations  under  Codes  of  Fair 
Competition,"  NRA,  Division  of  Review,  Work  Materials  No.  86,  1936. 

37.  G.  von  Haberler,  Der  Internationale  Handel  (Berlin,  1933) ,  p.  229;  (English  ed., 
1936) ,  p.  309. 

38.  This  is  one  reason  why  international  dumping  does  not  necessarily  presuppose 
the  protection  of  high  domestic  prices  by  duties.  Moreover,  the  most  advantageous 
price  discrimination  is  generally  such  that  it  does  not  pay,  in  any  case,  to  re-import 
cheap  exported  goods. 

39.  G.  Seidler,  "  The  Control  of  Geographic  Price  Relations  under  Codes  of  Fair 
Competition,"  NRA,  Division  of  Review,  Work  Materials  No.  86,  1936,  p.  33. 

40.  As  to  the  size  of  an  area  supplied  at  all:  If  h  is  the  maximum  degree  of  dumping 
technically   possible   under   the   basing-point   system    alone     (freight    from   factory   to 


Some  New  Factors  159 

be  smaller  as  a  rule  than  the  whole  absorbable  amount  in  the 
limiting  case  of  profit  plus  fixed  costs.  Thus  it  is  true  that  the 
basing-point  system  restricts  but  does  not  prevent  unreasonable 
dumping  into  a  foreign  area.  On  the  other  hand,  reasonable 
dumping  within  the  home  area  zuill  be  prevented,  though  in  varying 
degree  according  to  the  construction  of  the  basing-point  system." 

(dd)    Uniform  Prices.    Uniform  prices  are  less  advantageous  for 


basing  point) ,  unassociated  with  price  policy  A;  z  the  degree  granted  by  agreement; 
and  m  the  degree  economically  possible  (profit  plus  average  fixed  costs) ,  then  the 
seller  will  be  willing  to  ship  anywhere,  with  uniform  f.  o.  b.  prices,  if  m  and  z  are  at 
least  equal  to  h  (the  highest  value  of  h  in  absorbed  freight  will  be  reached  only  on 
the  extension  of  the  factory  basing-point  line  beyond  the  latter) .  'if  m  or  z  is  smaller 
than  h,  not  even  the  basing  point  itself  will  be  supplied.  With  a  straight  mileage 
tariff  in  a  uniform  transport  area  the  market  area  will  then  be  bounded  by  a  hyperbola. 
This  includes  the  basing  point  when  m  and  z  lie  between  h  and  h/2;  it  becomes  a 
straight  line  that  passes  halfway  between  factory  and  basing  point  when  z  is  equal  to. 
and  m  at  least  equal  to,  h/2,  or  vice  versa.  Conversely,  if  m  or  z  is  smaller  than  h/2, 
the  hyperbola  includes  the  factory  site.  In  the  latter  case,  however,  not  only  will  no 
freight  be  absorbed;  more  will  be  taken  in  than  when  freight  is  charged  as  of  factory 
(so-called  freight  advantage:  see,  for  example,  Moller,  Weltwirtschaftliches  Archiv, 
1943,  p.  91,  Fig.  1) .  With  a  sliding-scale  tarifl  [involving  lower  mileage  rates  for  longer 
hauls.— W.  H.W.]  the  hyperbolas  close  to  ellipsoid  curves  (G.  Mecklenburg,  Der  Giiter- 
transportaufwand  der  Deutsclien  Eisenindustrie,  Hannoversche  Dissertation  [1941],  p. 
27). 

On  the  size  of  an  area  supplied  to  special  advantage:  Besides  the  area  that  a  factory 
not  situated  at  the  basing  point  is  willing  to  supply  at  all,  that  part  of  an  area  that 
it  will  supply  with  more  profit,  and  that  other  part  that  it  will  supply  with  less  are 
of  interest;  or,  more  accurately,  that  part  that  it  will  supply  at  higher  or  lower  prices 
than  when  freight  is  charged  from  the  factory.  The  dividing  line  passes  halfway 
between  factory  and  basing  point  if  the  price  policy  in  both  places  is  the  same;  that  is, 
if  they  either  charge  the  same  uniform  f.  o.  b.  price  or  if  both  discriminated  starting 
from  the  same  level.  Prices  will  be  higher  via  the  basing  point  at  the  site  of  the 
fatcory,  and  vice  versa. 

On  the  other  hand,  if  equal  prices  are  charged  from  the  basing  point  and  dis- 
criminatory f.  o.  b.  prices  at  the  factory,  the  area  in  which  charges  via  the  basing  point 
result  in  higher  f.  o.  b.  prices  is  widened  (provided  z,  m  ^  h) .  Only  in  an  ellipsoid 
area  in  which  the  basing  point  itself  lies  excentrically  is  an  f.  o.  b.  price  policy  more 
advantageous.  The  ellipse  becomes  larger  when  the  starting  price  with  discrimination 
is  higher  than  the  uniform  basing-point  price,  and  smaller  in  the  opposite  case.  In 
short,  with  shipments  toward  the  basing  point  the  seller,  with  shipments  away  from 
the  basing  point  the  buyer,  pays  more  freight  than  with  rational  dumping.  Hence  in 
the  one  case  revenue,  in  the  other,  demand,  decreases  more  rapidly  with  distance. 

41.  With  a  uniform  basing-point  price,  producers  at  the  basing  point  cannot  differ- 
entiate their  factory  prices  at  all  according  to  the  distance  of  buyers.  Producers  who 
are  not  situated  at  the  basing  point  do  not  discriminate  directly  away  from  the  basing 
point,  but  toward  the  basing  point  they  discriminate  too  strongly  against  neighboring 
buyers.  (The  c.  i.  f.  price  falls  with  distance  from  the  factory  instead  of  rising,  though 
more  slowly  than  would  correspond  to  the  actual  freight.) 


j5o  Part  Two.     Economic  Regions 

the  seller  unless  they  considerably  facilitate  sales  promotion  and 
business  calculations.  Uniform  factory  prices  (F)  and  uniform 
delivered  prices  (C)  must  be  distinguished.  The  buyer  pays  the 
freight  in  the  former  case,  the  seller  in  the  latter.  Nevertheless,  it 
makes  no  difference  to  the  seller  (in  the  average  case  of  linear 
demand)  which  of  the  two  uniform  prices  he  selects,  so  long  as  his 
sales  area  is  determined  by  competition  and  not,  say,  by  govern- 
mental authority.  The  size  of  his  sales  area  and  thus  the  number 
of  independent  enterprises  as  well,  no  less  than  the  size  of  their 
profits,  will  be  the  same  in  either  case.*^  Sales  and  the  average  factory 
price  will  also  be  equal.  All  this  is  true  whether,  from  the  stand- 
point of  the  individual  firm,  the  tendency  toward  maximum  profits 
predominates;  or  whether,  from  the  standpoint  of  the  economy  as  a 
whole,  the  tendency  toward  maximization  of  the  number  of  inde- 
pendent business  units  predominates;  *^  in  other  words,  whether 
sales  areas  are  chosen  as  advantageously  as  possible,  or  as  small  as 
possible.** 

(ee)  Geographic  Price  Policy  and  Competition.  The  competi- 
tion of  old  and  of  new  enterprises,  that  is,  efforts  to  expand,  or  to 
begin  an  independent  existence,  must  be  sharply  distinguished.  The 
former  finds  its  geographic  limits;  the  latter  is  virtually  as  unlimited 
as  the  reservoir  of  those  who  would  like  to  make  themselves 
independent. 

1.  Competition  by  New  Enterprises.  We  have  developed  the 
various  possibilities  of  geographic  price  policy  for  the  case  where 
an  arbitrary  market  area  is  at  the  disposal  of  an  entrepreneur.  The 
tendency  to  keep  the  area  of  the  individual  enterprise  as  small  as 

42.  Thus  C  is  possible  not  only  with  goods  for  which  freight  plays  no  role.  The 
elimination  of  too  distant  buyers  is  caused  with  F  by  the  price,  with  C  by  the  refusal 
of  the  entrepreneur  to  deliver. 

43.  See  section  ee. 

44.  This  is  because  the  aggregate  demand  curve  and  the  aggregate  marginal  revenue 
curve  are  identical  with  F  and  C  for  both  the  uniform  and  the  average  f .  o.  b.  price. 
My  "  Geographie  der  Preise "  advances  the  difficult  proof.  The  intersection  of  the 
marginal  revenue  and  marginal  cost  curves  determines  the  most  favorable  uniform 
price.  In  Figure  45,  an  amplification  of  Figure  40,  if  Pq  is  the  uniform  f.  o.  b.  price, 
and  Pa  the  uniform  c.  i.  f.  price,  DPq  will  determine  the  sales  and  TP^  the  f.  o.  b.  price 
and  the  marginal  revenues  in  the  individual  localities  (points  of  intersection  with 
do,  di,  and  do,  and  Uq',  Ui',  and  u^'  respectively) .  EP^  gives  the  discriminatory  factory 
prices  for  the  case  where  aggregate  sales  are  as  they  are  with  C  and  F.  The  marginal 
revenues  from  all  buyers  are  the  same  (Q,  7?,5)  only  with  A;  with  T  {M,R,W)  and 
C  (A^,  R,  T)  ,  on  the  contrary,  they  are  partly  too  high  and  partly  too  low  to  permit 
an  equally  advantageous  exploitation  of  the  demand,  and  thus  an  equally  large  profit. 


Some  New  Factors 


161 


possible  prevails  only  in  an  open  market.  It  was  assumed  in 
Chapters  9-12  that  the  limit  had  been  reached  when  the  area  was 
so  diminished  that  the  demand  curve  at  a  uniform  factory  price  was 
tangent  to  the  cost  curve.  With  any  further  decrease  the  enterprise 
would  no  longer  cover  its  cost,  unless  it  adopted  the  expedient  of 
spatial  price  discrimination;   that  is,  unless  it  demanded  different 


Fig.  45.   Comparison  of  price  discrimination  (0),  uni- 
form f.  o.  b.  price  (V),  and  (X)  uniform  c.  i.  f.  price 

factory  prices  of  its  customers  according  to  their  distance.  This 
brings  in  additional  revenues.  These  do  not  always  permit  a  further 
reduction  in  the  market  area.  Such  a  reduction  becomes  more  and 
more  possible,  however,  the  greater  the  necessary  market  area  and 
the  greater,  therefore,  the  possibilities  for  freight  absorption.*^  Thus 

45.  To  determine  the  smallest  market  area  and  the  most  favorable  price  therein, 
the  marginal  cost  curve  is  no  longer  made  to  intersect  the  current  highest  marginal 
revenue  but  the  lowest  possible  one,  and  thus  the  one  that  is  valid  for  the  smallest 
possible  number  of  places.  It  need  not  be  the  lowest  absolutely,  if  in  such  a  small 
area  total  revenues  are  below  total  costs  throughout.  This  is  less  common  with  A, 
and  in  addition  the  chances  that  a  low  marginal  revenue  curve  here  would  be  inter- 
sected by  the  marginal  cost  curve  are  rather  better  because  the  former,  though  mathe- 
matically identical  with  the  curves  for  C  and  F,  is  significant  for  a  larger  area.   With 


,(j2  Part   Tivo.     Economic  Regions 

where  the  tendency  to  multiplication  of  independent  enterprises  is 
in  full  operation  it  compels  geographic  price  discrimination.^^ 

2.  Competition  by  Existing  Enterprises.  How  does  the  approach 
of  competition  affect  price  policy:  (a)  at  the  boundaries  of  the 
geographic  area  supplied,  and   {b)   in  general? 

(tti)  Will  the  compactness  of  areas  be  destroyed  by  dumping; 
or  (fls)  will  the  price  be  lowered  by  competition  to  variable  costs, 
at  least  on  the  boundary?  Or  (^3)  will  competitors  leave  to  each 
other  the  contributions  of  marginal  buyers  to  profit,  or  at  least 
to  fixed  costs?  Or  {b)  will  they  nevertheless  pursue  a  policy  in 
respect  to  the  general  level  of  their  prices  that  can  never  lead  to  a 
stable  equilibrium  of  their  prices  and  their  markets? 

Here  I  can  only  set  down  my  answer— not  give  reasons  for  it. 
{a)  The  tendency  toward  maximization  of  the  number  of  inde- 
pendent enterprises  forces  the  entrepreneur  with  sufficient  insight 
at  the  boundary  also  toward  price  discrimination  in  the  manner 
indicated,  {b)  Furthermore,  it  generally  leaves  but  little  room  for  a 
strategic  price  policy  as  developed  by  W.  Launhardt,*^  H.  Hotelling,^^ 
T.  Palander,*^  E.  Schneider,^"  and  others  with  respect  to  freight  costs, 
at  least  for  duopolists.^^  With  adequate  insight  there  usually  exists 
a  definite  equilibrium.   If  many  act  irrationally,  equilibrium  will  be 


A  smaller  areas  are  therefore  possible  than  with  C  and  F,  where  among  a  host  of 
identical  marginal  revenue  curves  one  lying  higher  than  with  A  will  often  be  decisive. 
There  would  be  so  much  to  say  in  explanation  here  that  I  refer  once  more  to  my 
forthcoming  "  Geographie  der  Preise."  Only  this  need  be  said  here:  That  marginal 
revenue  curves  should  be  identical  is  entirely  consistent  with  the  fact  that  the  total 
revenue  curves  with  A  lie  uniformly  higher. 

46.  If  the  tendency  to  a  multiplication  of  independent  enterprises  compels  price 
discrimination,  this  in  its  turn  encourages  an  increase  of  competition— either  local  or 
distant.  In  the  former  case,  more  firms  share  the  same  area;  in  the  latter,  the  area 
will  be  still  further  reduced  until  in  both  cases  profits  have  disappeared  despite  price 
discrimination.  Local  competition  need  not  prevent  price  discrimination  itself.  It  is 
enough  that  by  cutting  into  sales  it  raises  production  costs  so  high  that  profits  are 
consumed.  Price  discrimination  occurs  even  though  its  purpose  is  thus  thwarted.  The 
areal  diminution  provides  a  typical  example  of  monopolies  almost  without  teeth,  that 
may  practice  price  discrimination  in  their  areas  and  yet  be  unable  to  make  excess  profits, 
because  the  areas  that  they  control  absolutely  are  too  much  restricted  from  without. 

47.  W.  Launhardt,  Mathematische  Begrilndung  der  Volkswirtschaftslehre  (Leipzig, 
1885) ,  pp.  161  ff. 

48.  H.  Hotelling,  "  Stability  in  Competition,"  Economic  Journal,  1929. 

49.  T.  Palander,  Beitrdge  zur  Standortstheorie  (Uppsala,  1935),  pp.  231-253,  370-394. 

50.  E.  Schneider,  "  Bemerkungen  zu  einer  Theorie  der  Raumwirtschaft,"  Econo- 
metrica,  1935,  pp.  90  ff. 

51.  With  geographical  dispersion  each  has  perhaps  half  a  dozen  competitors,  and 
thus  has  a  moderate  influence  on  each  individually. 


Some  Nevj  Factors  163 

deferred,  whereas  knowledge  and  legal  encouragement  of  the  right 
behavior  will  lead  more  quickly  to  a  stable  and  rational  outcome." 
This  will  be  discussed  under  y?. 

52.  Concerning  a^:  Dumping  in  a  neighboring  area  would  be  countered  or,  still 
better,  averted,  so  that  the  aggressor  in  particular  would  rather  diminish  and  destroy 
his  own  profitability  once  the  endeavor  to  establish  new  plants  is  wholly  effective.  If  all 
dump,  then  of  course  the  necessary  minimum  size  of  market  is  increased,  but  so  also  is 
the  chance  of  still  invading  them  by  an  abandonment  of  dumping.  Only  in  competition 
with  different  goods,  therefore,  not  with  homogeneous  ones,  is  it  rational  to  absorb 
freight. 

Concerning  03:  The  following  holds  true  for  price  discrimination.  As  the  aggregate 
marginal  revenue  curve  is  shifted  to  the  left  with  the  diminution  of  an  area,  its  inter- 
section with  the  marginal  cost  curve  also  moves  toward  the  left.  According  to  whether 
the  new  point  of  intersection  is  higher  or  lower  than  the  old,  the  new  factory  price  at 
the  geographical  boundary  will  be  higher  or  lower  than  before.  In  the  new  equilibrium 
the  average  costs,  which  generally  rise  with  decreased  sales,  exceed  the  factory  price  at 
the  geographical  boundary.  Here  the  price  lies  between  average  and  marginal  costs. 
Marginal  costs  are,  of  course,  still  equal  to  the  marginal  revenue.  But  this  says  only 
that  variable  costs,  not  necessarily  all  the  fixed  costs  involved  as  well,  are  covered  by 
the  revenue  in  the  boundary  zone.  Indeed,  this  certainly  will  not  be  the  case,  and  the 
deficit  will  be  just  made  up  by  the  surpluses  in  the  vicinity  of  the  factory.  The 
"  exploitation  "  of  districts  near  the  factory  and  dumping  in  those  at  a  distance  com- 
pensate one  another.  Together  they  make  it  possible  to  decrease  the  necessary  market 
area  far  more  than  without  price  discrimination.  The  diminution  proceeds  until  the 
average  costs  are  so  high  above  the  factory  prices  prevailing  in  the  boundary  zone  that 
the  deficit  in  fixed  costs  is  only  just  covered  by  the  surpluses  in  the  interior. 

Concerning  b:  How  are  a  stable  price  and  market  to  be  found?  The  matter  is  not 
so  simple  that  one  need  only  advise  that  half  the  freight  be  added  to  the  costs.  For 
the  costs  depend  upon  the  size  of  the  area  also,  and  this  is  still  unknown.  Following 
the  example  of  Walras  with  his  "  prix  crie  par  hasard  "  in  a  one-point  market,  would 
it  not  be  possible  to  start  from  a  boundary  accidentally  held  between  areal  markets? 
Each  would  then  determine  the  most  favorable  starting  price  on  the  basis  of  his  costs 
and  his  share  of  the  demand  (A'  in  Figure  41)  .  Whoever  was  cheaper  than  his  com- 
petitors because  of  this  starting  from  an  arbitrary  boundary  would  as  a  rule  have  to 
move  the  boundary  back  until  prices  were  equal  there.  It  is  improbable  either  that 
the  cheaper  seller  should  retreat  of  his  own  accord,  or  that  the  boundary  (like  price 
in  the  Walrasian  market)  should  be  jointly  changed.  Each,  rather,  would  eagerly  hope 
for  a  market  area  of  the  most  advantageous  extent,  no  matter  whether  or  not  his 
competitors  were  located  in  it;  whether  he  would  therefore  have  to  drive  them  from 
the  market  or  share  it  with  them.  According  to  this  boundary,  as  he  imagines  it,  he 
sets  his  starting  price,  only  to  find  that  he  has  begun  with  too  large  an  area,  since  his 
competitors  will  underbid  him  before  he  reaches  that  boundary.  Each  one,  therefore, 
has  higher  costs  and  smaller  revenues  than  he  calculated,  so  each  generally  lowers  his 
sights  as  to  the  desirable  market  area  and  usually  raises  the  price.  Each  gropes  his  way 
toward  the  equilibrium  point  where  boundary  and  boundary  price  coincide.  Is  there 
only  one  such  boundary  and  boundary  price?  The  curve  of  delivered  prices  at  the 
boundary  for  all  boundary  points  on  the  line  connecting  "  I  "  and  "  II  "  at  which  "  I  " 
can  aim,  cuts  the  corresponding  curve  for  "  II  "  only  once  if  the  boundary  price  changes 
monotonically  with  shifting  of  the  boundary— which  upon  closer  examination  appears 
to  be  the  rule.  When  each  stops  struggling  and  cannot  expect  more  than  mere  existence 
where  there  is  a  strong  tendency  to  independence— stable  equilibrium  reigns. 


i6^  Part  Two.    Economic  Regions 


2.     EFFECTS  OF  GEOGRAPHIC  PRICE  POLICY 

(aa)  Effect  on  Density  and  Agglomeration  of  Locations.  With 
A  the  most  profitable  market  area  is  larger,  that  necessary  to  exis- 
tence equal  to  or  smaller  than  with  F  or  C.  Hence,  in  industries 
to  which  there  is  free  entry,  locations  will  often  lie  closer  together 
with  price  discrimination  than  with  uniform  prices. 

The  effects  of  price  policy  on  the  agglomeration  of  locations  in 
favored  regions  are  harder  to  assay.  First,  as  to  the  locations  of  the 
originators  of  the  policy:  With  A,  and  still  more  with  C,  the  profits 
from  neighboring  buyers  are  higher  than  those  from  more  distant 
ones.  Consequently  the  former  weigh  more  heavily  in  the  choice 
of  a  location  than  would  correspond  to  their  demand,  to  say  nothing 
of  their  number— one  more  reason  for  the  concentration  of  industries 
in  large  cities.  Most  important  are  the  effects  of  the  basing-point 
system:  Plants  situated  at  a  basing  point  enjoy  an  unlimited  market 
area.  Nowhere  can  they  be  undersold,  nowhere  can  they  lose;  but 
their  goal  is  the  highest  profit.  When  the  point  of  lowest  c.  i.  f.  costs 
does  not  coincide  with  the  basing  point  they  move,  like  all  plants, 
toward  it.^^  The  more  evenly  all  competitors  in  a  market  area  share 
the  demand,  the  more  nearly  do  the  points  of  least  c.  i.  f.  costs  for 
all  coincide.  They  agglomerate  until  some  costs  of  production  rise 
so  much  because  of  the  concentration  that  some  plants  migrate  to 
another  point  of  agglomeration.  Only  when  industries  voluntarily 
concentrate  in  a  smaller  market  area  (which  will  generally  be  more 
advantageous)  does  there  arise  a  tendency  to  disperse  from  the 
basing  point,  and  to  settle  more  densely  the  farther  they  scatter. 
Whether  dispersion  or  new  agglomeration  is  the  final  result,  migra- 
tion from  the  basing  point  is  probable.^* 

For  the  buyers  in  the  industry  whose  price  policy  is  under  con- 

53.  Here  is  a  striking  example  of  Weber's  theory  that  until  now  has  passed  unnoticed 
by  its  adherents.  An  enterprise  with  a  given  output  (quota)  ,  a  given  body  of  buyers 
who  can  nowhere  be  lost  to  cheaper  competitors,  and  a  particularized  demand  (since 
delivered  prices  are  stationary)  can  actually  choose  a  location  by  means  of  the  isoda- 
pane  diagram,  especially  when  the  prices  of  many  production  factors  are  geographically 
leveled  by  rate  schedules  and  stabilized.  The  minimum  transport  need  not  be  at  the 
site  of  consumption.  It  is  not  true,  therefore,  that  a  tendency  necessarily  develops  to 
move  from  the  basing  point  to  the  point  of  consumption  in  order  to  save  freight, 
which  the  customer  pays  anyway.  It  depends  upon  whether  or  not  the  freight  on  raw 
materials  is  increased  thereby. 

54.  According  to  A.  R.  Burns  the  capacity  of  the  iron  and  steel  industry  from  1916 
to  1931  rose  more  rapidly  outside  the  basing  point,  Pittsburgh  (The  Decline  of  Com- 
petition [New  York,  1936],  p.  341) . 


Some  New  Factors  165 

sideration,  the  advantages  are  reversed.  They  may  be  attracted  to 
or  toward  the  cheap  basing  point  or  (with  policy  A  and  especially 
F)  the  production  site,  but  this  is  likely  to  be  overshadowed  by  a 
host  of  other  factors.  Policy  C,  like  the  basing-point  system,  elimi- 
nates not  only  the  influence  of  the  producer's  location  on  prices, 
but  also  the  influence  of  prices  on  the  location  of  the  consumer. 
Within  the  sales  area  chosen  the  good  concerned  becomes  ubiqui- 
tous. Buyers  agglomerate  less  at  the  production  site;  but  whether 
they  will  then  disperse  or  concentrate  more  thickly  somewhere  else 
remains  undecided.  To  set  uniform  delivered  prices  is  to  eliminate 
the  most  important  regulator  of  a  rational  spatial  arrangement. 

(bb)  Effects  on  Producers  and  Consumers.  A  comparison  with 
price  discrimination  shows  that  A  almost  always  results  in  higher 
profits  and,  with  free  entry,  a  greater  number  of  independent  enter- 
prises.^^ Thus  it  is  more  advantageous  for  the  entrepreneur,  whereas 
F  always  results  in  lower  c.  i.  f.  prices,  and  so  on  the  average  favors 
the  consumer.^^  Only  distant  consumers  fare  better  with  A,  and 
better  still  with  C,  because  here  freight  is  absorbed;  those  living 
near  the  factory,  on  the  other  hand,  pay  higher  prices  (see  Fig.  45)  . 
With  the  basing-point  system  and  with  policy  C  much  waste  through 
cross-haulings  is  likely,^^  which  raises  prices. 

/?.   Price  Differentials  among  Different  Market  Areas 

If  factory  prices  and  freight  rates  with  policy  A  or  F  are  the  same 
for  all  production  centers,  as  we  have  assumed  so  far,  their  sales 
areas  are  equilateral  hexagons  and  their  boundaries  straight  lines. 
If  the  freight  rates  (straight  mileage  tariffs)  are  different,  the  sales 
areas  are  irregular  polygons  and  their  boundaries  are  arcs.  If  factory 
prices  are  different,  the  sales  areas  are  irregular  polygons  and  their 
boundaries  are  hyperbolic  arcs.^^  Practically,  this  is  perhaps  the  most 

55.  A.  Losch,  Geographie  der  Preise    (in  preparation)  . 

56.  One  may  be  undecided  whether  to  interpret  this  to  mean  that  the  demand  curve 
of  a  certain  area  in  respect  to  the  average  c.  i.  f.  price  is  lowest  with  F  and  highest 
with  C.  Consumers  are  more  heavily  overcharged  with  A  and  C,  but  also  they  are 
prepared  to  pay  more. 

57.  Especially,  also,  within  the  district  around  a  basing  point  in  which  producers  are 
located  and  in  which  in  the  transport  system  is  already  subjected  to  heavy  strains. 

58.  This  is  easily  seen,  even  without  algebraic  proof.  To  points  on  the  boundary  it 
must  be  a  matter  of  indifference  from  which  of  the  neighboring  production  centers 
they  order.  The  constant  differences  in  factory  price  must  therefore  be  compensated 
by  an  equally  constant  and  opposite  difference  in  freight.  But  the  geometric  locus  of 
all  points  whose  distances  from  two  given  points  differ  by  a  constant  amount  is  a 
hyperbola.    In  so  far  as  prices  are  lowest  in  the  metropolis,  the  hyperbolas  lie  with 


i56  Part  Two.    Economic  Regions 

important  case.  Finally,  if  both  factory  prices  and  freight  rates  are 
different,  the  sales  areas  are  irregular  polygons,  and  their  boundaries 
are  curves  of  the  fourth  degree.'^  The  boundary  lines  become  still 
more  complicated  if  the  straight  mileage  tariff  is  replaced  by  a 
graduated  tariff. 

The  situation  is  entirely  similar  for  regions  of  agricultural  supply 
except  that  they  are,  so  to  speak,  the  mirror  image  of  industrial  sales 
areas.  If  the  boundaries  of  the  latter  are  projections  of  sections  of 
price  funnels,  agricultural  boundaries  originate  in  the  intersection 
of  price  cones.  Again  the  case  of  equal  freight  rates,  but  different 
prices  at  the  centers,  is  the  most  important  one.  Figure  46  shows  the 
price  cone  for  three  places,  A,  B,  and  C,  and  above  S  the  industrial 
mirror  image.  In  exactly  the  same  way  that  B,  as  an  industrial  place, 
would  be  excluded  from  sales  if  the  price  there  were  equal  to  the 
price  at  A  plus  the  freight  costs  from  A  to  B,  it  would  be  prevented 
from  supplying  agricultural  products  if  the  price  at  B  were  equal 
only  to  the  price  at  A  less  the  freight  from  B  to  yl.^°  Just  as  the 
line  DG"  forms  the  upper  limit  of  industrial  production,  so  DG  is 
the  lower  limit  for  agricultural  production  at  the  price  in  B.  The 
larger  a  town,  the  higher  the  market  price  of  agricultural  products 
in  it.  Assuming  that  the  population  of  A  doubled,  the  price  of  milk, 
say,  would  have  to  rise  above  AD  in  order  that  the  milkshed  could 
increase  at  the  expense  of  town  B.  B,  too,  would  experience  a  price 
increase,  but  by  a  smaller  absolute  amount  because  its  population 
has  remained  the  same.  Consequently  the  branches  of  its  bounding 
hyperbola  will  be  more  compressed:  it  carves  out  for  its  own  needs  ®^ 


their  vertices  toward  the  center  of  the  areal  system.  Moreover,  they  intersect  in  such 
a  way  that  their  foci  lie  about  in  the  middle  of  the  areas  that  they  enclose.  For  then 
then  demand  is  greatest. 

59.  W.  Launhardt  has  already  shown  this  (Mathematische  Begriindung  der  Folks- 
wirtschaftslehre  [Leipzig,  1885],  pp.  157  f.) .  T.  Palander  has  given  a  detailed  derivation 
(Beitrdge  zur  Standorttheorie  [Uppsala,  1935],  pp.  223-230.  See  also  his  Fig.  193,  p.  363). 
Moreover,  A.  Schilling  ("  Die  wirtschaftsgeographischen  Grundgesetze  des  Wettbewerbs 
in  mathematischer  Form,"  Technik  und  Wirtschaft,  XVII  [1924],  p.  146)  introduces 
in  addition  market  boundaries  ("  isostants  ")  between  a  point  and  an  economic  front, 
which  likewise  are  conic  sections— ellipses,  parabolas,  or  hyperbolas.  They  do  not  arise 
geometrically  as  with  competition,  between  two  points  by  the  intersection  of  price 
funnels,  but  by»  the  intersection  of  a  price  funnel  with  a  plane  representing  the  c.  i.  f. 
price,  which  rises  from  the  economic  front  outward  by  the  amount  of  the  freight  costs. 

60.  Unless  B  were  on  a  traffic  route  that  connected  A  with  its  hinterland. 

61.  A.  Predohl  ("  Die  ortliche  Verteilung  der  amerikanischen  Eisen-  und  Stahl- 
industrie,"  Weltwirtschaftliches  Archiv,  XXVII,  239-292,  and  314*-329*)  has  described 
the  corresponding  industrial  case.  As  long  as  B  (Chicago)  does  not  fully  meet  the 
local  demand  for  steel,  A  (Pittsburgh)  will  supply  the  rest  and,  being  the  marginal 
producer  determine  the  price  until  Chicago  produces  enough,  and  more  than  enough. 


Some  New  Factors 


167 


a  smaller  area  of  the  milkshed  supplying  A.  The  milkshed  of  C, 
a  still  smaller  town,  lies  within  that  of  B.  As  there  are  other  towns 
lying  beside  B  and  C,  their  supply  areas  actually  will  not  extend 
up  to  the  circular  arcs,  but  will  be  already  bounded  by  further 
branches  of  the  hyperbolas. 


woyyw 


Fig.  46.     Price  cones  for  agricultural  products  around  towns 
A,  B,  and  C,  and,  above  the  5-axis,  their  industrial  mirror  image 

It  is  different  with  price  policy  C.  If  every  producer  of  a  standard- 
sized  product  asks  a  uniform  c.  i.  f.  price,  different,  however,  from 
that  of  his  competitor,  the  cheapest  producers  would  extend  their 
sales  areas  in  all  directions  up  to  the  most  advantageous  sales  radius. 
Farther  out  they  will  refuse  deliveries,  even  though  they  are  cheaper 
than  their  competitors.^^ 


for  local  demand  at  the  Pittsburgh-plus-price.    Then  the  price  will  drop  in  Chicago 
and  it  will  have  its  own  sales  area. 

62.  No  diminution  of  areas  occurs  in  this  case.  The  competition  of  those  already 
established  reacts  on  the  competition  of  new  entrants  in  such  a  way  that  it  affects  the 
particular  individual  rather  than  the  number  of  competitors— until  the  new  entrants 
change  to  policy  A  or  F,  which  are  more  profitable  for  them. 


j58  Part  Two.    Economic  Regions 


§2.     Local   Product   Differentiation 

Although  spatial  price  discrimination  enables  market  areas  to 
become  very  small,  spatial  product  differentiation  counteracts  this 
effect.  Only  a  few  goods  are  homogeneous  when  produced  in  dif- 
ferent places.^2  As  a  rule  they  satisfy  jointly  a  number  of  require- 
ments that  do  not  exactly  coincide.  Not  even  the  main  requirement 
need  be  the  same:  thus,  independent  of  price,  a  car  is  a  necessity 
in  one  place  and  a  pure  luxury  elsewhere;  to  say  nothing  of  the 
way  in  which  it  meets  needs  with  various  models,  for  example,  or 
satisfies  minor  needs,  as  with  seats  that  can  be  thrown  back  for 
sleeping.  The  character  of  an  article,  among  other  things,  is  a 
function  of  its  production  site,  and  conversely.  It  is  designed  in 
accordance  with  the  cost  and  demand  relationships  prevailing  there. 
The  demand  that  it  is  intended  to  meet  generally  comes  from  the 
immediate  neighborhood  of  its  production  site,  though  not  exclu- 
sively as  with  homogeneous  goods.  The  boundaries  of  its  sales  area 
no  longer  coincide  with  those  of  the  neighboring  production  sites. 
The  market  areas  overlap.  For  even  though  the  majority  of  buyers 
lived  near  the  factory  and  its  product  conformed  to  the  require- 
ments of  the  neighborhood,"*  there  would  still  be  individual  pur- 
chasers farther  off  who  for  various  reasons  preferred  just  this  type 
of  article  to  one  manufactured  in  their  own  vicinity.  Migration  is 
not  the  least  important  contributor  to  this.  Often  enough  migrants 
are  pioneers  of  exportation.''^  So  common  taste  creates  about  every 
factory  a  circle  of  buyers  that  overlaps  in  space  the  sales  areas  of 
similar  products.*'®   The  individual  nature  of  a  product  thus  works 

63.  The  difference  may  lie  in  the  type  of  retail  business  rather  than  in  the  goods 
themselves.  Retail  trade  margins,  and  with  therp  the  price  for  the  same  product,  vary 
according  to  the  type  of  business.  In  the  more  expensive  shops  one  pays  for  the 
possibility  of  making  a  number  of  other  purchases  at  the  same  time,  for  their  better 
equipment  with  all  that  this  implies,  or  for  the  certainty  of  receiving  high-quality, 
tasteful,  or  fashionable  goods,  and  so  on. 

64.  Not  necessarily  the  most  immediate  neighborhood,  if  the  factory  is  in  a  small 
place.  For  in  an  unrestricted  area  most  of  the  demand  would  then  come  from  a 
medium  distance,  according  to  Fig.  43c. 

65.  In  the  United  States  this  tendency  is  counteracted  by  the  extremely  high  tariff 
on  the  one  hand,  and  by  the  extremely  low  price  of  domestic  mass-produced  goods  and 
transportation  on  the  other.  Without  them  this  "  melting  pot  of  the  nations  "  would 
hardly  have  been  able  to  bring  about  uniform  production  so  quickly.  It  is  interesting 
to  observe  the  effect  of  similar  factors  in  Germany:  strangulation  of  foreign  trade, 
"  Volks "  radios,  the  Volkswagen,  directed  consumption,  cheaper  travel  through 
"  Strength  through  Joy,"  and  so  on. 

66.  Something  similar  occurs  also  in  the  cultural  field,  and  is  perhaps  at  the  root 


Some  New  Factors  169 

both  for  and  against  a  manufacturer:  for  him  because  he  can  invade 
the  field  of  his  competitors  in  spite  of  freight  costs;  against  him 
because,  in  spite  of  his  more  favorable  freight  position  he  cannot 
keep  the  competition  of  similar  goods  entirely  out  of  his  home 
area.®^  The  more  unique  an  article  is  and  the  fewer  substitutes  it 
has,  the  less  does  it  have  its  market  entirely  to  itself.*^^  But  for  the 
same  reason  its  market  area  is  very  much  larger  than  if  all  its  buyers 
lived  in  the  same  place.®®  How  many  sales  areas  overlap  may  be 
realized  from  the  great  variety  of  goods  carried  by  retail  dealers. 

Entrepreneurial  activity  also  can  be  understood  spatially.  Small 
improvements  extend  the  home  sales  area  at  the  expense  of  com- 
petitors and  make  it  more  concentrated.  New  or  greatly  improved 
goods  capture  their  market  at  the  expense  of  all  old  goods  together. 
Thus  the  development  of  the  automobile  took  place  at  the  expense 


of  the  described  phenomenon.  The  more  local,  national,  or  even  racial  cultures  sur- 
render their  peculiar  character;  the  more  wide  differences  give  way  to  harmless 
nuances  that  practically  exhaust  themselves  in  different  dialects,  a  few  idiosyncrasies 
in  customs  and  costume,  and  the  fading  memory  of  a  different  past;  the  more  do 
regions  of  influence  of  different  cultural  centers  overlap.  They  were  separated  as  long 
as  the  differences  were  real,  and  would  be  separate  again  if  these  differences  vanished 
entirely;  but  in  this  intermediate  stage  they  overlap. 

67.  It  is  hard  to  say,  threfore,  whether  product  differentiation  takes  the  edge  off 
competition,  as  is  so  often  asserted.  It  seems  to  me  that  it  intensifies  competition  for 
the  efficient  and  protects  the  inefficient.  Sensible  though  it  may  be  to  have  real 
differences,  it  is  senseless  if  not  harmful  when  inefficient  producers  are  able  to  maintain 
themselves  through  insignificant  variation  in  product  or  even  through  adulterations 
that  the  customer  can  hardly  detect. 

68.  Hence  the  markets  for  raw  materials  and  semifinished  products  overlap  less  than 
those  for  finished  products,  because  they  are  still  relatively  amorphous  and  so  can 
often  be  standardized.  In  addition,  freight  costs  are  more  important  for  the  former 
in  relation  to  the  producer's  price,  so  that  for  this  reason  alone  overlapping  is  restricted 
to  a  narrower  border  region.  With  high-quality  goods  everything  often  depends  upon 
specific  properties  of  the  raw  material,  which  then  is  ordered  from  a  great  distance 
even  though  ordinary  grades  may  be  plentiful  enough.  Thus  hundreds  of  German 
places  can  supply  clay,  but  only  one  can  furnish  the  clay  needed  for  the  making  of 
highly  fire-resistant  products. 

In  the  case  of  finished  products,  and  especially  of  consumer's  goods,  the  small 
standard  goods  in  daily  use  that  are  distributed  from  small  centers  with  fairly  compact 
sales  areas  must  be  distinguished  from  more  expensive  goods  in  which  the  possibility 
of  choice  and  subtle  differences  are  valued,  and  which  therefore  can  be  stocked  only 
in  larger  places  with  less  sharply  circumscribed  sales  areas.  See,  for  example,  C. 
Zimmerman,  "  Farm  Trade  Centers  in  Minnesota,  1905-1929,"  University  of  Minnesota, 
Agricultural  Experiment  Station  Bulletin  269,  1930,  p.  16. 

69.  An  extension  of  the  sales  area  at  the  expense  of  competitors  or  of  other  goods 
can  thus  occur  in  many  and  very  different  ways:  {a)  by  displacement  outward  of  its 
farthest  boundaries;    (b)   by  extension  of  the  actual  sales  area  within  these  boundaries; 

(c)   by  larger  sales  in  the  original  area,  partly  to  old  and  partly  to  new  customers. 


j„„  Part  Two.     Economic  Regions 

not  only  of  the  railroads  but  also  of  the  manufacture  of  pianos, 
beverages,  and  so  on.  Later,  when  a  new  product  has  become  an 
economic  success,  imitators  will  share  its  market  area.  If,  on  the 
contrary,  this  was  too  small  even  for  the  first  entrepreneur  (i.  e., 
if  he  could  not  make  the  demand  and  the  cost  curves  intersect) , 
he  counts  as  one  of  the  pioneers  who  failed.  Between  the  one  market 
of  the  entrepreneurial  genius  and  the  rigidly  circumscribed  areas  of 
enterprises  that  produce  standard  goods,'"  development  moves  back 
and  forth. 

§3.    The   Freight   Rate 

With  public  enterprises,  monopoly  freight  rates  often  aim  only 
for  certain  services  at  the  greatest  profit;  "  with  others,  at  covering 
the  costs;  "  while  a  third  group  is  deliberately  subsidized.  The  pre- 
vailing German  railway  tariff  offers  examples  of  each.  A  graduated 
tariff  is  not  essential  to  any  of  the  three  principles.  Only  the  extent 
of  the  graduation  shows  which  is  in  question."  As  far  as  location 
is  concerned  the  most  important  case  of  a  subsidy  in  Germany  is 
certainly  long-distance  transport  of  coal.  It  breaks  up  agglomerations 
around  coal  fields,  which  the  increasing  use  of  machinery  and  exhaus- 
tion of  the  forests  had  encouraged  during  the  past  century.'*  Some- 
thing similar  is  true  for  important  raw  materials.'^ 

But  only  competitive  tariffs  follow  general  rules.  Next  to  a  drop 
in  the  level  of  freight  rates  to  about  1/10,'^  differential  railway  rates 

70.  For  example,  steel,  cement,  bricks,  coal,  salt,  sugar,  and  so  on.  Even  here,  to  be 
sure,  there  are  exceptions.  Certain  furnaces,  for  instance,  utilize  the  caloric  content 
of  certain  kinds  of  coal  better  than  others.  To  this  extent  there  is  still  some  over- 
lapping.  But  the  cores  of  the  sales  areas  of  the  various  coal  fields  are  distinct. 

71.  Especially  with  busy  stretches,  moderate  distances,  small  shipments,  and  expen- 
sive goods    (see  note  77)  .    In  these  cases  the  competition  of  the  motor  truck  enters. 

72.  The  significance  of  fixed  costs  for  a  railroad  is  generally  much  overestimated, 
and  the  height  of  the  marginal  costs  therefore  underestimated.  With  fully  employed 
equipment  every  traffic  increase  must  raise  costs  almost  proportionately.  It  is  generally 
impossible  to  justify  cheap  special  rate  schedules  of  wide  applicability  with  low  mar- 
ginal costs.   I  shall  discuss  this  subject  in  more  detail  in  another  book. 

73.  When,  in  1924,  the  cheapest  railway  kilometer  for  the  cheapest  commodity  was 
about  1  per  cent  of  the  most  expensive  kilometer  for  the  most  expensive  commodity, 
the  one  was  obviously  subsidized  and  the  other  profitable. 

74.  W.  Sombart,  Die  moderne  Kapitalismus,  II  (1919)  ,  1143  ff.;  Ill  (1927) ,  98  f.,  122. 

75.  Other  things  being  equal,  the  use  of  machinery  must  nevertheless  decrease  with 
the  distance  from  coal,  and  so  must  the  production  of  low-quality  mass-produced  goods 
with  distance  from  raw  material;  on  the  contrary,  the  importance  of  poorly  paid  labor 
of  high  quality  must  increase. 

'76.  W.  Sombart,  op.  cit.,  II,  345.  P.  Schulz-Kiesow,  Die  Eisenhahngutertarifpolitik 
in  ihrer  Wirkung  auf  den  industriellen  Standort  und  die  Raumordnung  (Heidelberg, 
1940) ,  p.  25. 


Sotne  New  Factors  171 

according  to  product  ^^  and  distance  constituted  the  most  significant 
change  for  the  location  pattern  since  the  exit  of  the  horse  and 
wagon,  which,  like  the  autotruck,  charged  freight  essentially  in 
proportion  to  weight  and  distance. 

a.   Local  Differences  in  Tariffs 

1.     GRADUATION     ACCORDING    TO    DESTINATION 

Suppose  that  goods  are  to  be  shipped  from  one  place,  B,  to 
others  at  various  distances.  The  elasticity  of  the  volume  of  traffic 
with  respect  to  the  freight  rate  will  rise,  first  with  this  rate,  and 
second  with  length  of  haul.^^  For  the  second  reason  a  monopolistic 
enterprise  lowers  the  freight  rate  for  long  hauls.  The  spatial  freight 
discrimination  of  a  graduated  tariff  corresponds  to  the  spatial  price 
discrimination  for  the  goods. 

Figure  47,  together  with  Figure  20,  will  serve  as  a  proof.  For 
the  sake  of  simplicity  assume  that  only  a  single  customer  lives  at 
each  place.  If  OP  (in  Fig.  20)  is  the  price  at  the  factory,  the  volume 
of  traffic  to  each  outlying  point  would  be  PQ  (in  Figs.  20  and  47) 
if  the  seller  paid  the  freight  or  if  the  freight  rate  were  zero.  The 
volume  of  traffic  is  zero  when  the  product  of  distance  times  freight 
rate  is  equal  to  or  greater  than  PF  (in  Fig.  20) .  Thus  the  farther 
away  a  place  is,  the  lower  is  the  freight  rate  that  suffices  to  prevent 
all  traffic.  If  Cq,  Ci,  62  (Fig.  47) ,  and  so  on,  are  demand  curves  for 
shipment  to  increasingly  distant  points,  they  become  flatter  and 
flatter  in  this  order  and  so  more  and  more  elastic  for  the  same 
freight  rate.  That  graduated  tariff  (i.  e.,  the  particular  set  of  freight 
rates  for  transports  over  different  distances)  which  maximizes  the 
surplus  of  receipts  over  variable  costs    (PR)     (Fig.  47)  ^^  is  easily 

77.  From  the  standpoint  of  maximizing  profits  what  matters  is  transportability  of 
goods,  not  their  value.  Salt  can  stand  higher  freight  charges  than  furniture,  although 
it  is  much  cheaper  by  the  pound.  The  reaction  of  consumers  as  well  as  of  the  producer 
is  important:  whether  new  production  sites  will  be  established  and  distances  shortened 
thereby  because  of  an  increase  in  freight  rates. 

78.  Elasticity  depends,  in  sales  areas,  upon  the  willingness  of  buyers  to  pay  the 
price  demanded;  in  supply  areas,  upon  the  chances  of  profit  to  the  seller.  According 
to  Lenschow  the  types  of  goods  produced  by  the  Negroes  in  British  East  Africa  pay 
more  freight  than  those  produced  by  the  white  inhabitants,  because  the  same  profit 
means  more  to  the  Negroes  and  it  is  harder  for  them  to  susbtitute  other  possibilities. 

79.  This  is  the  exact  meaning  of  the  saying  that  railways  exact  as  freight  "  what 
the  traffic  will  bear."  The  lower  limits  of  the  freight  rate  are  the  variable  costs.  The 
rate  is  not  arbitrarily  fixed  above  this  level,  but  in  such  a  way  that  the  surplus  for 
the  individual  case  shall  be  as  large  as  possible.  The  total  surplus  must  be  at  least 
equal  to  the  fixed  costs,  otherwise  the  whole  industry  will  be  unprofitable. 


172 


Part  Two.    Economic  Regions 


obtained  by  the  customary  procedure:  In  Figure  47  draw  RS  parallel 
to  PQ  and  halve  the  segment  of  the  demand  curve  lying  between 
RS  and  the  ))-axis.  The  graduated  tariff  will  lie  on  the  line  RA 
connecting  these  points. 

The  effect  of  the  graduated  tariff  upon  the  size  of  the  necessary 
market  areas  differs.  For  short  distances  the  graduated  tariff  lies 
above,  for  long  distances  below,  a  tariff  proportional  to  distance.   If, 


Volume  of  traffic 


Fig.  47.  Similarity  of  price  differen- 
tiation for  goods  and  spatial  freight 
differentiation  through  zonal  tariffs 

under  free  competition,  the  latter  just  covers  the  costs,  the  tariffs 
intersect  at  a  greater  distance  than  if,  with  a  monopoly,  a  tariff 
proportional  to  distance  gave  the  same  total  profit.  The  effect  of  a 
graduated  tariff  on  the  size  of  the  necessary  market  area  depends 
upon  whether,  for  shipment  to  the  boundaries  of  the  necessary  sales 
area  with  a  tariff  proportional  to  distance,  the  graduated  tariff  lies 
above  or  below  the  tariff  proportional  to  distance.  If  it  lies  above, 
and  all  local  prices  are  therefore  higher  and  the  regional  demand 
is  accordingly  less  than  with  a  tariff  proportional  to  distance,  the 
necessary  sales  area  will  be  larger  with  a  sliding-scale  tariff.  But  if 
the  sliding-scale  tariff  lies  at  the  critical  point,  considerably  below 
the  tariff  proportional  to  distance,  a  smaller  sales  area  may  suffice. 
Hence  it  cannot  be  said  a  priori  whether  a  graduated  tariff  en- 
courages ^°  or  discourages  industrial  concentration.  The  influence 
of  a  sliding-scale  tariff  on  the  possible  shipping  distance  (which  it 
naturally  extends)    must  not  be  confused  with  its  influence  on  the 


80.  M.  Keir  insists  that  it  does.  ("  Economic  Factors  in  the  Location  of  Manufac- 
turing Industries,"  Annals  of  the  American  Academy  of  Political  and  Social  Sciences, 
1921,  p.  90.) 


Sofne  New  Factors  i73 

necessary  shipping  distance,  an  influence  which  is  usually  ^^  decisive 
in  itself.  As  freight  costs  increase  but  slowly  over  long  distances 
with  a  sliding-scale  tariff,  large  areas  arise  in  which  the  superiority 
of  one  particular  producer  depends  merely  upon  small  differences 
in  the  c.  i.  f.  price.  This  is  enough  when  products  are  homogeneous. 
But  even  slight  product  differentiation  leads  to  an  unstable  equi- 
librium and  extensive  regional  overlap.^- 

In  a  few  cases  the  freight  rate  increases  with  distance.  This  is 
true,  for  example,  of  firms  that  make  deliveries  by  their  own  motor 
trucks.  If  their  customers  are  more  than  a  day's  trip  away,  the  cost 
of  delivery  is  increased  by  overtime  and  lodgings. ^^  The  effects  are 
the  reverse  of  a  sliding-scale  tariff. 

2.     GRADUATION     ACCORDING    TO     POINT     OF     ORIGIN 

A  tariff  graduated  according  to  the  point  of  origin  can  be  thought 
of  by  imagining  that  various  means  of  transportation  radiate  out 
from  different  points,  or  that  the  same  carrier  grants  special  rate 
schedules  to  certain  places,  or  that  the  difference  is  due  to  the  nature 
of  the  goods  transported.  For  instance,  with  the  same  rate  per  ton, 
a  rich  ore  pays  less  freight  per  unit  of  yield  (unit  of  useful  content) 
than  a  poor  ore. 

What  is  the  relation  between  the  sales  areas  of  two  places  that 
ship  the  same  product  under  different  freight  rates?  In  generAl  two 
things  may  be  said.  First,  the  product  with  the  lower  tariff  cannot 
be  entirely  excluded  from  sale,  whatever  its  factory  price  may  be. 
Even  though  it  is  displaced  at  its  own  production  site  by  anothei 
article  that  can  be  made  much  more  cheaply,  with  a  sufficiently 
large  possible  sales  area  a  point  is  nevertheless  reached  at  some  dis- 
tance where  the  delivered  price  of  the  product  paying  the  lower 
rate  falls  below  that  of  the  other.**  Second,  the  sales  area  of  the 
place  with  the  higher  tariff  will  be  surrounded  by  that  of  the  other. 
It  is  naturally  smaller  the  higher  the  freight  rate  and  the  higher  the 
factory  price.  It  may  shrink  to  a  mere  point  and,  in  contrast  to  the 
other  area,  disappear  entirely. 

81.  With  mining  outputs  the  actual  and  the  possible  shipping  distances  may  perhaps 
coincide.  The  sales  area  for  Rhenish  pumice  stone,  for  example,  is  limited  only  by 
the  freight,  not  by  direct  competition. 

82.  See  T.  Palander,  Beitrdge  zur  Slandortsthcorie   (Uppsala,  1935)  ,  p.  365. 

83.  As  the  result  of  a  fairly  good  investigation  J.  Schmitz  calculated  that  this  point  is 
reached  for  the  brewing  industry  at  a  sales  radius  of  about  47  miles.  {Das  Standortproh- 
lem  in  der  deutschen  Brauereiindustrie,  University  of  Cologne  dissertation,  1930,  p.  61). 

84.  See  the  figures  in  Palander,  op.  cit.,  p.  228. 


174 


Part  Two.    Economic  Reg-ions 


/3.   Level  of  the  Freight  Tariff  Schedule 

We  come  now  to  the  case  where  the  tariff  is  raised  or  lowered, 
not  for  single  points  but  for  all.^^  If  the  freight  level  falls,  the  pos- 
sible size  of  sales  areas  is  increased,  but  the  minimum  necessary 
size  is  decreased.^^  For  the  lowered  freight  lowers  the  c.  i.  f.  prices, 
and  as  a  consequence  there  now  comes  from  the  original  sales  areas 
a  demand  that  is  greater  than  necessary.  Lowered  freight  rates 
permit  smaller  sales  areas. 

There  are  several  reasons  for  the  prevalent  belief  that  reduced 
freights  extend  markets.  First,  an  erroneous  one:  The  possible 
shipping  distance  is  regarded  as  equal  to  the  reasonable  one.  For  the 
possible  shipping  distance  the  following  propositions  hold  true:  ^^ 
The  shipping  distance  in  kilometers  is  inversely  proportional  to  the 
freight  rate;  the  sales  area  and  the  sales  are  inversely  proportional 
to  its  square.®^  But  that  this  enormous  effect  of  lowered  freights 
can  never  be  actually  exerted  is  easily  seen  from  the  fact  that  it 
benefits  competitors  also,  and  the  cheaper  competitor  more.  His 
sales  area  expands,  chiefly  at  the  cost  of  his  more  expensive  rivals,^^-^" 
a  few  of  whom  may  be  driven  completely  from  the  market.  But 
this  is  not  the  end  result,  for  now  profits  appear  that  induce  the 
establishment  of  new  factories,  and  these  finally  cut  down  sales  areas. 

85.  On  goods  with  a  large  necessary  shipping  distance  the  sliding  scale  tariff  operates 
in  many  respects  as  a  general  lowering  of  the  rate  schedule. 

86.  For  example,  the  automobile  has  increased  the  possible  sales  radius  of  retail 
business  almost  tenfold,  but  certainly  not  the  economic  sales  radius. 

87.  See  D.  Lardner's  century-old  Railway  Economy  (London,  1850) ,  p.  14.  W. 
Launhardt's  paradoxical  conclusion,  that  lower  freight  rates  increase  sales  areas  greatly 

{Mathematische  Begriindung  der  Volkswirtschaftslehre  [Leipzig,  1885],  p.  152)  but 
supply  areas  hardly  at  all  (ibid.,  p.  177)  ,  rest  upon  the  fact  that  in  Thiinen's  case  the 
number  of  consumers  (i.  e.,  the  population  of  a  town)  is  constant,  whereas  with 
industrial  sales  it  can  be  increased  as  long  as  competition  is  not  considered,  and  is  in 
fact  increased  in  the  case  of  monopolistic  industries.  An  example  is  the  extension  of 
rural  mail  delivery  with  motorization.  See  Heberle's  beautiful  maps  in  Weltwirtschaft, 
1934,  p.  15,  and  for  the  opposite  opinion,  C.  Pirath,  Die  Grundlagen  der  Verkehrswirt- 
schaft   (Berlin,  1934) ,  p.  73. 

88.  In  contrast  to  price  policy  F  the  possible  sales  with  A  are  thus  increased  fourfold, 
and  with  C  to  infinity.  Of  course  a  general  lowering  of  freight  does  not  increase  sales 
so  much  as  the  individual  demand  curve  might  lead  one  to  expect. 

89.  Similarly,  the  sales  area  expands  for  goods  that  are  cheaper  to  produce  but 
more  expensive  to  ship  (Fig.  3) .  Agricultural  materials,  for  example,  are  more  fre- 
quently processed  at  some  central  location. 

90.  Launhardt  {op.  cit.,  p.  160)  wrote  that  with  improvements  in  communication 
the  more  expensive  product  loses  "  the  most  effective  of  all  protective  tariffs,  the  pro- 
tection of  bad  roads."  Hence  protectionism  rises  with  the  lowering  of  freight  rates. 
Conversely,  an  increase  in  freight  rates  benefits  the  more  expensive  producers  because 


Some  New  Factors  ^75 

The  new  competition,  however,  may  now  have  to  arise  "  within  "— 
that  is,  at  the  location  of  the  cheap  factories— because  immobile 
conditions  of  production  are  now  more  important  than  freight.^^ 

In  such  a  case  the  sales  area  would  retain  its  increased  size,  but 
more  factories  would  share  the  same  market.  To  this  extent  the 
lowering  of  freight  rates  really  does  further  the  concentration  of 
production,»2  especially  where  the  supply  of  labor  is  favorable.^^ 

The  cheapening  of  transportation  has  likewise  extended  the 
market  areas  for  similar  goods,  because  here  the  actual  approaches 
the  possible  shipping  distance.  (A  sociological  parallel  would  be 
a  widening  of  the  circles  between  which  marriages  occur.)  This 
intensifies  true  competion,  just  as  overlapping  markets  for  similar 
goods  intensify  senseless  competition. 

One  more  exception  to  our  thesis  is  possible.  Suppose  there  are 
two  methods  of  manufacturing  a  certain  product,  of  which  one  is 
cheaper  only  with  very  large  sales.  The  planning  curve  would  then 
divide  into  two  branches,  tti  and  ira  in  Figure  48;  it  is  broken. 
Suppose  further  that  at  the  old  freight  rate  even  the  entire  possible 


freight  becomes  more  important  in  relation  to  production  costs.  The  guiding  maxim 
of  medival  road  policy,  "  The  worse  the  roads  the  higher  the  profits,"  thus  benefited 
inferior  producers  only.  Their  business  prospered  under  the  protection  of  inconspicu- 
ousness  and  seclusion. 

Launhardt  has  formulated  this  double  effect  of  cheaper  freights  with  classic  brevity. 
Reduction  of  freight  rates  decreases  the  importance  of  distance.  "  Mastery  over  space 
has  been  extended,  and  all  activities  that  were  hampered  in  their  development  by 
spatial  restrictions  have  been  broadened  and  advanced  in  consequence;  on  the  other 
hand,  all  that  required  the  protection  of  isolation  have  been  curtailed  and  enfeebled  " 
(ibid.,  p.  206)  . 

91.  Local  characteristics  are  now  more  sharply  developed.  Thus  the  effects  of  a 
lowering  of  transport  costs  are  by  no  means  only  leveling. 

Agricultural  production  is  afifected  in  the  same  way  by  lower  freight  rates,  resources 
like  soil  quality,  climate,  or  cheap  labor  gaining  in  significance  as  compared  with  site. 
The  intensity  of  agriculture  decreases  on  land  near  cities.  In  the  nineteenth  century 
many  scattered  and  rather  unproductive  mines  closed  down  and  mining  was  concen- 
trated at  the  cheapest  deposits;  this  contributed  to  the  agglomeration  of  the  iron 
industry,  which  once  had  flourished  in  many  places.  The  great  general  lowering  of 
rail  and  ocean  freights,  together  with  special  reductions  for  long  hauls  and  raw 
materials,  made  it  the  general  practice  at  that  time  to  obtain  many  raw  materials  from 
the  most  favorable  sources.  If  the  natural  productivity  of  a  soil  becomes  thus  more 
important  the  lower  the  freight  rates,  then,  conversely,  the  location  of  a  country  plays 
a  smaller  role  the  richer  it  is  by  nature. 

92.  As  for  the  effect  on  consumption,  lower  freight  rates  diminish  price  differences 
and  with  them  also  differences  in  supply,  as,  conversely,  a  reduction  of  shipping  space 
in  wartime  again  increases  spatial  differences  in  supply. 

93.  On  the  other  hand,  the  artificial  leveling  of  wages  nowadays  raises  the  impor- 
tance of  even  low  freight  rates. 


176 


Part  Two.     Economic  Regio7is 


sales  area  has  been  too  small  to  make  cheap  mass  production  possible. 
Ai  has  not  intersected  tts.  But  with  a  lowering  of  the  freight  rate, 
sales  in  the  old  area,  as  well  as  the  possible  area  itself,  are  greatly 
increased.  Now  A2  intersects  tt^,  and  cheap  mass  production  becomes 
profitable.  Now,  too,  the  area  can  be  decreased  again  until  A2'  is 
tangent  to  the  curve  tto.  It  is  now  possible,  though  not  necessary, 
that  the  new  area  is  larger  than  the  old. 


k 

v\ 

^/^ 

^ 

jij 

\ 

\ 

^;s. 

y 

Y' 

V 

<^ 

\^2 

Amount 

Fig.   48.    Effect   of  new   large-scale 
economies  on  size  of  market  area 

The  extraordinary  reduction  in  transportation  costs  during  the 
nineteenth  century  has  most  probably  had  this  effect  in  general,^* 
but  it  must  not  be  forgotten  that  two  phenomena  were  then  working 
together:  first,  improvements  in  large-scale  production  (ttz  supplants 
TTi  at  a  certain  volume  of  production)  ;  and  second,  improvements 
in  transportation  and  communication   (A2  replaces  Ai)  .^^    Had  not 


94.  An  increase  in  population  or,  more  accurately,  in  buying  power,  acts  in  this 
respect  like  a  lowering  of  freight  rates.  This  explains  in  particular  the  fact  that 
businesses  are  larger  in  cities  than  in  rural  areas,  not  smaller,  as  one  might  at  first  be 
led  to  expect  since  the  urban  demand  curve  is  generally  steeper  and  therefore  touches 
the  old  cost  curve  at  a  point  characterized  by  higher  price  and  smaller  sales.  For  this 
reason,  on  the  other  hand,  the  reduced  demand  in  wartime  often  favors  the  small 
producer. 

A  further  reason  why  many  prices  are  lower  in  cities  may  be  that  cities  attract  a 
number  of  the  most  skillful  entrepreneurs,  who  find  it  possible  to  employ  their  capabil- 
ities to  the  full  only  in  large  cities;  either  (when  they  are  especially  skillful  in 
production)  because  they  lower  the  cost  curve,  or  (when  they  are  especially  skillful 
in  advertising)  because  they  shift  the  demand  curve  to  the  right— both  of  which  lead 
to  a  lowering  of  prices. 

95.  They  belong  to  the  six  great  events  that  have  revolutionized  locations  during 
the  nineteenth  century:  (1)  increase  in  population;  (2)  monopolies  based  on  inven- 
tions; (3)  the  change  from  wood  and  water  power  to  coal;  (4)  the  exhaustion  of 
smaller  sources  of  raw  materials  through  a  sharp  increase  in  production;  (5)  further 
mechanization;  (6)  lowering  of  freight  rates.  These  factors  favored  the  following 
locations,  though  they  partly  counteracted  one  another:  coal  deposits  (3, 5) ;  large  and 


Some  New  Factors  ^77 

the  two  coincided  (which  certainly  was  not  mere  chance) ,  the  fate 
of  those  worlds  in  miniature  whose  unquestioned  center  was  a 
princely  residence,  a  small  rural  town,  or  often  only  a  manor  house, 
would  not  have  been  fulfilled  so  soon.  At  it  was,  most  of  their 
central  functions  were  transferred,  perhaps  all  too  quickly,  to  the 
potential  centers  of  larger  areas.^^  This  generally  brought  down  the 
price  of  centrally  produced  goods,  but  at  what  cost!  The  world  in 
miniature,  which  had  been  so  clear  to  the  understanding,  so  easy  to 
survey,  fell  in  ruins.  The  "  province  "  became  part  of  a  greater 
whole  that  in  its  wide  expanse  was  at  first  much  more  difficult  to 
grasp,  much  more  abstract.  The  attitude  toward  life  did  not  broaden 
in  step  with  this  technical  expansion."  This  was  true  not  only  in 
quiet  corners  remote  from  the  metropolis  but,  much  more  impor- 
tant, in  the  metropolis  itself.  The  unmanageable  specialization  in 
central  functions  impeded  not  only  their  close  touch  with  the  rural 
areas,  but  their  mutual  fructification  as  well.  Individual  functions 
were  fulfilled  more  cheaply  and  more  and  more  practically— which 
of  course  was  the  reason  for  this  rearrangement— but  society  as  a 
whole  suffered  at  first  an  increasingly  thorough  uprooting.  The 
great  drop  in  freight  rates  tore  the  towns  away  from  their  regions. 
In  America  especially,  every-day  goods  are  frequently  ordered  from 
fantastic  distances,  because  of  small  differences  in  quality,  or  in 
order  to  circumvent  the  seasons:  potatoes  from  Idaho,  lettuce  from 
California,  cabbage  from  Texas,  flowers  from  Florida.®^  Here  it  may 


I 


cheap  sources  of  raw  materials  (4,6);  cities  (1,5,6);  supply  of  labor  (6);  arbitrarily 
selected  sites  (1,2).  See,  for  example,  W.  Sombart,  Der  moderne  Kapitalismus,  I  5.  A 
(1922);  113.  A  (1919);  IIIl.A  (1927).  O.  Schlier,  Der  deutsche  Industriekorper  seit 
1860.  Tiibingen,  1922.  H.  Ritschl,  "  Reine  und  historische  Dynamik  der  Erzeugungs- 
zweige,"  Schmollers  Jahrbuch,  1927.  P.  Schulz-Kiesow,  Die  Eisenbahngutertarifpolitik 
in  ihrer  Wirkung  nnf  den  industriellen  Standort  und  die  Raumordnung  (Heidelberg, 
1940) . 

The  expansion  of  many  markets  in  the  nineteenth  century  was  itself  part  of  a 
greater  chain  of  developments  that  was,  however,  not  free  of  reverses.  Beginning  with 
specialization  (handicrafts  on  socage  farms  and  in  villages) ,  continued  by  urbanization 
(guilds  against  rural  crafts)  ,  and  accelerated  by  mechanization  (factory  against  crafts) , 
it  ended  with  the  double-edged  victory  of  mass  production  (large  against  small  enter- 
prises) that  results  here  and  there  in  a  reduction  in  the  size  of  markets  (controlled 
markets  and  autarky)  . 

96.  The  subordination  of  a  once  independent  center  to  a  larger  one,  or  of  a  depen- 
dent center  to  a  different  main  center,  affects  the  central  upper  stratum  most  severely, 
for  with  it  the  changes  in  either  location  or  function  are  greatest. 

97.  Or  accepted  it  only  in  externals.  Ropke  has  much  that  is  just  to  say  against 
this  rising  "  cult  of  the  gigantic." 

98.  See,  for  example,  E.  A.  Buddy's  investigation  of  this  subject  in  respect  to 
Chicago:  "  The  Physical  Distribution  o?  Fresh  Fruits  and  Vegetables,"  University  of 
Chicago,  Studies  in  Business  Administration,  Vol.  VII,  No.  2. 


i>j8  Part  Two.    Economic  Regions 

be  asked  whether  food  grown  in  the  very  soil  on  which  we  live  may 
not  agree  with  us  better,  and  the  most  recent  investigations  tend 
to  favor  this  view. 

To  summarize  the  purely  economic  effect  of  lower  freight  rates: 
Though  in  general  they  reduce  the  size  of  economic  areas,  under 
certain  conditions  they  increase  their  size.^^  A  reduction  in  freight 
rates  affects  only  the  size  of  individual  towns,  however,  not  their 
geographical  distribution.  For  the  variety  of  possible  market  areas 
remains  unchanged  by  lowered  freight  rates  as  long  as  the  distribu- 
tion of  farms  is  unchanged.  Only  the  individual  products  are  now 
associated  with  areas  of  another  size.  Only  the  distance  between 
their  production  sites  is  altered,^""  whereas  the  possible  sites  for 
factories  remain  as  before.  Hence  the  economic  function  of  towns 
changes  with  changes  in  the  cost  of  transportation  in  so  far  as 
entirely  different  goods  are  now  sold  in  the  market  areas  whose 
centers  they  are;  but  the  possible  market  areas  themselves  and  the 
situation  of  their  centers  remain  as  they  were. 

b.     NATURAL    DIFFERENCES 
§1.     Local   Differences   in    Producti  vit  y  i<>^ 

We  now  dismiss  the  assumption  of  a  uniformly  fertile  plain,  and 
take  into  account  the  fact  that  nature  favors  human  endeavor 
unequally  from  place  to  place.  Production,  cultivation,  or  acqui- 
sition is  possible,  according  to  the  manner  in  which  she  co-operates: 
manufacture  or  building  when  nature  supplies  only  resources  (indus- 
try) ;  cultivation  when  man,  on  the  other  hand  increases  natural 
fertility  (agriculture)  ;  and  collection  when  the  desired  products  are 
already  present    (mining,  fishing,  and  the  like) . 

The  kind  and  degree  of  nature's  co-operation  may  vary  from  one 
place  to  another  in  the  most  irregular  way,  or  in  conformity  with 
some  rule,  or  may  be  entirely  uniform  over  wide  areas.  The  fre- 
quency of  the  first  situation  causes  many  to  despair  of  any  spatial 

99.  If  it  is  desired  to  encourage  industry  in  an  outlying  district  where  conditions  of 
production  are  not  especially  favorable,  it  follows  that  (except  for  raw  materials) 
incoming  freight  rates  should  not  be  lowered;  but  (where  freight  decrease  reduces  the 
size  of  one  area)  the  rates  within  it,  or  (where  freight  decrease  increases  the  size  of 
the  area)   from  it  to  the  rest  of  the  country,  should  be  lowered. 

100.  Large  losses  or  gains  may  occasionally  be  caused  by  the  shift:  losses,  if  necessary 
sales  areas  increase  in  size,  for  then  the  concentrated  industries  suddenly  appear  over- 
crowded; gains,  if  necessary  market  areas  grow  smaller,  because  it  always  requires  some 
time  for  the  influx  to  fill  vacancies  in  thes  branches. 

101.  Their  economic  significance  has  been  worked  out  with  the  greatest  care  by 
E.  W.  Zimmermann,  among  others,  in  World  Resources  and  Industries  (New  York,  1933). 


Some  New  Factors  i79 

economic  pattern.  The  irregularities  of  nature  do  indeed  interrupt 
the  uniform  development  of  landscapes.  But  they  need  not  destroy 
it  entirely,  since  all  the  organizing  forces  combine  against  the 
separate  chaotic  ones.  For  instance,  even  if  soil  quality  differed 
radically  from  field  to  field  its  use  would  not  show  the  same  mosaic 
confusion;  the  differences  would  be  modified  here  and  there  by  the 
effects  of  equal  distance  from  a  market,  by  the  establishment  of 
belts,  and  so  forth.  But  even  if  these  were  of  no  great  moment 
cmd  farming  and  the  rural  population  were  irregularly  distributed, 
a  superstructure  of  rural  towns  and  larger  settlements  would  never- 
theless spring  up  and  remain  separate  despite  everything,  which,  in 
spite  of  all  distortion,  would  still  form  a  pattern,  and  which  would 
orient  themselves  toward  the  metropolis  and  the  great  lines  of 
communication. 

Regular  changes  in  natural  conditions  are  obviously  much  less 
disturbing,^"^  and  by  good  fortune  they  are  both  common  and 
important.  One  need  only  recall  the  climatic  changes  associated 
with  latitude,  or  the  fairly  uniform  variations  in  the  lines  of  equal 
precipitation  over  wide  stretches  of  the  earth's  surface.  Precipitation 
is  of  definite  importance  in  the  United  States,  for  example,  where 
it  decreases  from  east  to  west;  or  in  southwest  Australia,  where  it 
decreases  toward  the  interior.  Natural  gradients  such  as  these  can 
be  found  even  in  zones  that  appear  economically  uniform.  Thus 
harvest  time  in  the  American  cotton  belt  varies  (or  shifts)  with  fair 

regularity  from  early  July  in  the  south  to  the  end  of  October  in  the 
north.103 

If  interruptions  of  the  sort  first  described  cause  a  certain  irregu- 
larity and  those  of  the  second  group  cause  inequalities  of  the  spatial 
economic  pattern,  the  interference  to  be  discussed  now  does  not 
appear  at  all  as  such  over  wide  areas.  Thus  there  are  extensive 
regions  of  more  or  less  equal  fertility  close  to  others  with  a  wholly 
different  level  of  productivity,  as  when  a  mountain  chain  rises 
suddenly  from  a  plain.  If  plain  and  mountains  are  extensive  enough, 
two  regions  may  arise  that  exhibit  great  regularity  within  them- 
selves but  which  are  characteristically  different.^"* 

102.  In  Weber's  words,  they  influence  the  choice  of  a  location  continuously,  like 
freight  costs,  not  alternatively,  like  local  advantages  that  occur  without  transition. 

103.  As  possible  supply  areas  for  cities  are  extensive  today,  they  often  include 
regions  with  entirely  different  harvest  dates  for  the  same  crop.  For  instance.  New  York 
gets  oranges  and  grapefruit  from  Florida,  from  Texas,  and  from  California  at  different 
times. 

104.  Such  regions  developed  in  the  lowland  indentations  about  Paris,  Cologne, 
Miinster,  Leipzig,  and  Breslau.    The  centers  for  the  corresponding  interlocking  high- 


i8o  Part  Two.     Economic  Regions 

Here  we  are  interested,  first,  in  these  differences  and,  second, 
in  the  conditions  at  the  border.  First,  are  market  areas  in  the 
fertile  ^"^  region  smaller  or  larger,  and  are  the  towns  more  numerous 
or  larger  than  in  the  poor  region?  The  answer  and  the  reason  for 
it  are  the  same  as  those  for  the  consequences  of  a  general  reduction 
in  freight  rates:  It  depends  upon  whether  there  are  fundamentally 
different  kinds  of  mass  production,  between  which  no  transition  is 
possible.  If  they  exist,  the  market  areas  on  the  fertile  soil  may  pos- 
sibly be  more  extensive  and  the  towns  larger.  If  they  do  not  exist, 
or  if  they  are  profitable  even  on  the  poor  soil,  then  the  market  areas 
will  be  smaller  ^"^  and  the  towns  more  numerous  on  the  rich  soil.^°^ 


lands  are  Trier,  Kassel,  Prague.  See  Blum,  "  Deutschland  und  Siidosteuropa  nach 
Riickgliederung  der  Ostmark  und  der  Sudetenlander,  verkehrspolitisch  betrachtet, 
Zeitschrift  fur  Verkehrsivirtschajt,  XVI    (1939),  1-31. 

105.  The  difference  between  small  and  large  holdings  of  land,  between  proximity 
to  and  distance  from  the  center  of  a  landscape,  between  peace  and  war  economy,  and 
often  between  greater  and  lesser  population  density,  is  equivalent  to  that  between 
more  and  less  fertile  soils.  On  a  more  fertile  soil  the  agricultural  population  is  always 
denser  and  (which  is  not  the  same)  the  villages  larger  (since  a  small  acreage  is  enough 
for  the  agriculturist  the  distance  to  the  fields  nevertheless  remains  tolerable) .  Large 
villages  make  possible  more  or  cheap  production  of  goods  that  are  bought  from  nearby 
than  do  smaller  villages. 

106.  They  are  smaller  the  more  closely  the  necessary  shipping  distance  approaches 
the  possible  one.  For  sales  areas  on  poor  soil  contain  relatively  much  land  but  a  small 
demand.  A  sales  area  in  a  thickly  settled  region  need  not  even  be  large  enough  to 
have  the  same  demand  as  that  of  the  more  thinly  settled  one.  Since  the  demand  in  a 
smaller  sales  area,  other  things  being  equal,  is  less  elastic  (as  has  already  been  shown) , 
a  firm  in  a  populous  region  can  always  cover  its  costs  despite  further  curtailment  of  the 
area  by  raising  prices.  Conversely,  however,  the  sales  areas  in  the  thinly  settled  region 
are  not  large  enough  to  result  in  the  same  demand  at  the  same  factory  price  as  sales 
areas  for  the  same  goods  in  the  other  region.  They,  too,  may  be  curtailed,  and  an 
adequate  demand  nevertheless  be  achieved  by  a  lowering  of  prices. 

Figure  49  resolves  this  apparent  contradiction,  r^  and  r^  are  demand  curves  in  a 
thickly  settled  region  {R) ,  a^  and  a^  in  a  thinly  settled  one  {A).  The  necessary  demand 
in  A  is  DE.  The  demand  curve  r^  would  result  in  R  in  the  same  demand,  DE,  at  the 
price  as  in  A.  But  the  corresponding  area  would  be  larger  than  with  the  curve  r^, 
which  lies  to  the  left  of  it  and  which  results  in  BC,  the  minimum  demand  necessary 
in  R.  The  same  thing  holds  true  when  sales  areas  in  A  are  compared  with  those  in  R. 
It  follows  that  the  prices  of  industrial  goods  in  the  towns  of  a  thinly  settled  region 
will  be  somewhat  lower.  Conversely,  the  prices  of  agricultural  products  in  the  towns, 
and  perhaps  even  average  rural  ground  rents,  will  be  somewhat  higher  than  in  a 
thickly  settled  region;  first,  because  freight  rates  are  higher  on  account  of  the  less 
intensive  use  of  the  means  of  communication;  second,  because  the  agricultural  supply 
area  for  the  towns  is  larger  since  they  are  more  populous;  and,  third,  because  that 
supply  area  itself  is  less  fertile. 

107.  Moreover,  goods  may  appear  here  for  which  there  would  not  be  an  adequate 
market  in  a  thinly  settled  region,  even  with  full  exploitation  of  their  possible  shipping 
distances. 


Some  iSJew  Factors 


This  does  not  mean  a  difference  in  size,  but  only  in  distribution 
of  the  population.  Other  things  being  equal,  the  number  of  inhabi- 
tants will  obviously  be  greater  on  fertile  soil. 

Second,  if  a  factory  lies  on  the  border,  the  size  of  that  part  of  its 
sales  area  extending  into  the  rich  or  the  poor  region  respectively 
will  depend  on  the  relative  size  of  markets  in  the  region  concerned. 
If  the  markets  are  large  in  the  poor  and  small  in  the  rich  region 
the  real  hinterland  of  the  factory,  measured  by  areal  extent,  will 
lie  in  the  former.  But  in  their  economic  value  both  regions  are 
about  the  same.  Because  of  their  irrational  shape,  such  border  areas 
are  on  the  whole  somewhat  larger  than  interior  areas.  If  sales  areas 
in  the  rich  region  are  larger,  it  is  uncertain  whether  a  factory  on 
the  border  will  attract  sufficient  demand  from  the  poor  region  to 
produce  on  the  larger  scale  of  the  fertile  region. 


Fig.  49.  Comparison  of  mar- 
ket area  in  thickly  settled  and 
thinly  settled  regions,  with 
equal  cost  curves 

Still  another  case  of  natural  differences  of  an  areal  kind  is  impor- 
tant. Imagine  a  large  region,  A,  and  a  small  one,  B,  wholly  similar 
in  natural  features  but  separated  by  a  wide  uninhabited  region  like 
a  mountain  range,  a  desert,  or  a  body  of  water,  or  by  high  customs 
duties  in  A.  The  essential  assumptions  are  the  differences  in  size 
and  distance.  Two  further  assumptions  are  economic  in  character. 
First,  the  planning  curve  must  have  a  break,  as  in  Figure  48.  Thus 
there  must  be  two  different  production  methods:  large-scale  and 
small-scale  production.  Second,  only  B  must  be  too  small  for  mass 
production.  Under  these  conditions  A  is  the  indicated  location  for  a 
large  plant. 

B  may  constitute  part  of  its  sales  area,  but  enterprises  can  never 
be  situated  in  B  and  supply  A  as  well.  According  to  the  assumptions, 
a  large-scale  enterprise  in  B  cannot  depend  upon  B  alone  for  its 
support.    In  A,  however,  it  is  too  expensive  by  the  amount  of  the 


I 


xgo  Fart   Two.     Economic  Regions 

freight  compared  with  a  local  large-scale  business,  even  if  there  are 
no  customs  duties.  But  a  large  enterprise  would  be  able  to  maintain 
itself  in  A,  either  if  A  were  an  adequate  sales  area  or  if  its  costs 
were  less  than  those  of  the  small  firm  in  B  by  more  than  the  amount 
of  the  freight. 

The  situation  would  suffice  to  make  the  United  States  the  classic 
land  of  large-scale  enterprises,  even  without  its  fantastic  customs 
duties."^  Of  all  the  European  countries,  Germany  most  nearly 
approaches  it  today  as  a  large  economic  area.^*'^  The  decisive  factor 
is  less  the  size  of  a  population  than  the  national  income.  The  other 
European  countries  would  lie  xvithin  the  market  areas  of  many 
large  American  businesses  if  they  did  not  "  protect  "  themselves  by 
customs  duties.^" 

Uniformly  operative  natural  factors  will  be  more  important  in 
general  for  agriculture,  irregular  factors  for  industry  and  mining. 
But  the  influence  of  nature  plays  a  significant  role  in  all  branches 
of  the  economy  in  the  formation  of  "  districts  "  and  "  belts."  "^ 
This  has  both  advantages  and  disadvantages:  disadvantages  in  so  far 
as  it  encourages  urbanization  and  causes  an  irrational  distortion 
in  the  shapes  of  market  areas;  advantages  in  so  far  as  the  external 
economics  that  result  when  similar  production  is  concentrated  in 
one  place  need  not  be  purchased  by  carrying  out  part  of  this  pro- 
duction under  unfavorable  natural  conditions. ^^- 

§2.     Local   Differences    in    Accessibility 

Among  the  purely  economically  conditioned  deviations  from  our 
initial  scheme  it  should  have  been  mentioned  that  a  transport  surface 
(i.  e.,  an  area  within  which  transportation  between  any  two  arbitrary 
points  is  always  possible  over  a  direct  route)  does  not  exist.  The 
limited  number  of  roads  and  railways  lines,  of  railroad  stations  and 

108.  Essentially  similar  conditions  make  large  cities  the  favored  sites  for  large-scale 
businesses.  The  metropolis  corresponds  to  the  United  States,  provincial  towns  to  the 
European  countries,  and  the  open  country  to  the  ocean. 

109.  Written  before  the  autumn  of  1939,  but  retained  in  the  1944  edition.— W.  H.  W. 

110.  See  A.  Losch:  Selbstkosten-  und  Standortverschiebungen  von  Genussgiltern  nach 
dem  Krieg  ah  Ursachen  von  Zolltendenzen  (Berlin,  1934)  (Zwischenstaatliche  Wirt- 
schaft,  edited  by  H.  v.  Beckerath,  Heft  4) . 

111.  5.  W.  Wilcox,  Chief  Statistician  of  the  Bureau  of  Labor  Statistics  in  Wash- 
ington, D.  C,  told  me  that  an  attempt  to  divide  Illinois  into  areas  of  similar  production 
showed  a  surprising  agreement  with  geological  structure,  which  went  so  far  that  regions 
where  corn  was  grown  for  the  market,  for  example,  were  associated  with  a  formation 
different  from  those  where  it  was  used  as  fodder. 

112.  It  would  be  so,  for  instance,  if  all  kinds  of  soil  were  evenly  mixed  everywhere. 


Some  New  Factors  i°3 

harbor  facilities,  can  be  ascribed  to  their  high  fixed  cost  if  to  nothing 
else.  Thus,  in  reality,  transportation  is  not  possible  between  any 
two  given  points  over  any  desired  route,  but  only  between  a  few 
so-called  transport  points  and  over  a  few  so-called  transport  lines. 
Still,  the  number  of  these  points  and  lines  varies  with  the  means 
of  transportation."^  It  is  large  in  the  case  of  wagons  and  motor 
trucks,"*  smaller  in  the  case  of  railways."^  and  smallest  in  the  case 
of  airplanes  and  ships.    Their  position  results  "^  essentially  from 

113.  For  the  laws  according  to  which  transport  is  distributed  among  the  various 
carriers,  and  the  relative  size  of  their  loads,  see  A.  Losch,  "  Die  Leistung  der  See- 
schiffahrt,"  Nauticus,  1941,  pp.  326-336. 

114.  The  narrow-meshed  network  of  highways,  with  stopping  places  wherever 
desired,  approaches  a  true  transport  surface  more  closely  than  the  wide-meshed  railway 
lines.  This  feature  of  motor-truck  transportation  is  especially  important  in  its  com- 
petition with  the  railways  and  in  the  development  of  locations.  If,  in  addition,  the 
characteristic  tariff  schedule  (according  to  straight  distance  and  weight,  not  sUding- 
scale  or  according  to  value)  is  taken  into  consideration,  the  most  important  results  of 
motorization  can  easily  be  deduced.  In  so  far  as  it  lowers  freight  costs  it  favors  places 
with  low  production  costs,  as  does  any  decrease  in  freight  rates.  In  so  far  as  it 
equalizes  freight  rates  it  works  to  the  disadvantage  of  "  favored  points,"  as  already 
shown.  Thus  no  simple  answer  can  be  given  to  the  disputed  question  of  whether  the 
motor  truck  has  a  centralizing  or  a  decentralizing  effect.  It  facilitates  access  to  and 
from  newly  developed  and  unfavorably  situated  places,  for  example.  On  the  one  hand, 
metropolitan  competition  can  now  break  into  remote  corners  and  destroy  local  industries. 
According  to  both  German  and  American  experience  this  seems  to  be  true  of  retail 
trade  especially.  (See  A.  Erlenmaier,  "  Die  Bedeutung  des  Kraftwagens  fiir  den  Standort 
in  Produktion  und  Handel,"  Zeitschrift  fiir  Verkehrswissenschaft,  XII  [1934];  and  C.  E. 
Lively,  "  Growth  and  Decline  of  Farm  Trade  Centers  in  Minnesota,  1905-1930,"  Uni- 
versity of  Minnesota,  Agricultural  Experiment  Station,  Bulletin  287.)  On  the  other 
hand,  favorable  production  conditions  may  attract  industries  to  formerly  inaccessible 
places  once  they  have  been  opened  up  by  the  motor  truck.  (For  examples  see  Erlen- 
maier, op.  cit.,  p.  94;  and  Palander,  op.  cit.,  pp.  352-360.)  In  a  similar  manner  the 
construction  of  railways  once  benefited  outlying  sources  of  labor.  (See  O.  Schlier,  Der 
deutsche  Industriekorper  seit  1860  [Tubingen,  1922];  and  P.  Schulz-Kiesow,  Die  Eisen- 
bahngiitertarifpolitik  in  ihrer  Wirkung  auf  den  industriellen  Standort  und  die  Raum- 
ordnung  [Heidelberg,  1940].) 

As  for  superhighways,  the  Autobahnen  of  Germany,  they  resemble  raihoads  in  that 
the  number  of  their  junction  points  is  limited.  Hence  in  comparison  with  ordinary 
highways  they  save  more  time  the  greater  the  distance  between  starting  point  and 
destination  and,  obviously,  the  nearer  both  lie  to  the  Autobahnen.  Lines  of  equal 
time-saving  run  like  arrowheads  toward  the  destination.  The  angles  are  considerably 
more  acute  in  the  case  of  the  Autobahnen,  to  be  sure,  than  they  once  were  with  the 
railways;  i.  e.,  the  latter  signified  a  much  -greater  revolution  of  communication.  See 
the  highly  interesting  maps  of  C.  Pirath,  "Auflockerung  und  Ballung  im  Lichte  der 
Reichsautobahnen,"  in  Volk  und  Lebensraum,  edited  by  K.  Meyer  (Heidelberg,  1938) , 
pp.  262,  269. 

115.  Three  out  of  four  German  communities  are  without  railway  station! 

116.  As  a  reaction,  of  course,  there  is  a  tendency  to  concentration  along  a  few  well- 
developed  traffic  routes,  especially  with  expensive  railway  installations. 


i84 


Part  Two.    Economic  Regions 


our  ideal  system  of  market  areas;  that  is  to  say,  from  transport 
requirements  proper— as  long  as  disturbances  brought  about  by 
nature  are  absent. 

a.    Transport  Lines 

Natural  obstacles  divert  transport  lines  according  to  the  law  of 
refraction,  which  is  valid  far  beyond  the  sphere  of  economics/^^  Man 
subjects  himself  to  it  by  choice  (after  all,  it  is  merely  the  economic 
principle  applied  to  a  special  situation)  ;  nature  (light  and  sound) 
by  necessity.    Here  is  a  significant  identity  between  a  law  of  nature 


Fig.  50.  The  law  of  refraction 

and  a  law  based  on  reason,  which  shows  clearly  enough  that  the 
economic  principle  is  not  merely  a  human  invention  and  does 
not  simply  correspond  with  the  attitude  of  a  particular  epoch.^^^ 
It  runs  through  the  history  of  natural  science  as  lex  parsimoniae: 
the  principle  of  simplest  means  or  least  resistance;  as  the  hypothesis 
that  natural  events  reach  their  goals  by  the  shortest  route. "^ 

Suppose  that  a  product  is  to  be  shipped  as  cheaply  as  possible 
from  A  to  B  (Fig.  50) .   North  of  the  coastline  CD,  which  is  equally 


117.  I  have  already  referred  to  this  in  my  review  of  Palander  ("  Beitrage  zur 
Standortstheorie,"  Schmollers  Jahrbuch,  1938)  .  In  the  meantime  appeared  the  detailed 
and  admirable  accoimt  of  H.  von  Stackelberg,  "  Das  Brechungsgesetz  des  Verkehrs," 
Jahrbiicher  fiir  Nationalokonomie  und  Statistik,  CXLVIII,  680-696. 

118.  On  the  contrary,  it  embraces  the  behavior  of  some  men  in  almost  all  situations, 
and  the  behavior  of  almost  all  men  in  some  situations:  when  desire  and  aversion  are 
strong  (one  wants  to  attain  a  definite  end  or  avoid  it  as  far  as  possible— pursues  every 
advantage  or  high  aim;  husbands  his  powers;  avoids  the  unpleasant)  .  It  is  otherwise 
when  we  live  everything  instead  of  separating  means  and  ends;  when  we  rejoice  in 
the  game;  surrender  ourselves  completely— only  those  can  do  so  who  are  free  of  desire 
and  filled  with  love.    There  are  two  worlds,  and  we  are  wanderers  between  them. 

119.  Others  of  our  results,  too,  have  their  counterparts  in  nature.  What,  after  all, 
are  the  often  sharply  separated  feeding  grounds  of  various  animal  families  and  species, 


Some  New  Factors  185 

favorable  everywhere  for  landing,  the  cheap  ocean  freight,  fa,  is  in 
effect;  south  of  it,  the  high  rail  freight,  /&.  The  transport  costs 
per  unit  for  the  distance  AE  will  then  be  Fa  =  fa\/a^ -\- {c  —  x)^; 
and  for  EB,  F^  =  /&V&'  +  x-.   F  (x)  =  F„  +  F^  is  a  minimum  when 

F{x)  =  -===  +  -^^=  =  «•   Hence  U  sin  ^  -  /«  sin  a  =  0, 

yj a^ -\- {c  —  x)-       y/h^-\-x- 

or  ^^"  '^  =  ft .    This  determines  the  site  of  the  harbor  jE.    If  the 
smj3       fa 

distance  per  unit  of  time  is  substituted  for  the  distance  per  unit  of 

freight  in  this  formula,  the  formula  for  the  refraction  of  light  and 

sound  will  be  obtained. 

Suppose,  thirdly,  that  an  officer  has  to  lead  his  troops  from  A  to 
B  with  the  smallest  possible  losses,  and  the  severity  of  the  enemy's 
fire  in  the  two  zones  is  related  as  the  freights  in  the  example  above. 
He  will  choose  route  AEB.  In  short,  the  formula  for  refraction  is 
universally  valid  when  two  unequally  favorable  zones  have  to  be 
crossed  with  the  smallest  expenditure,  whether  of  time,  money, 
blood,  or  the  like.  The  most  important  application  of  the  law  of 
refraction  is  probably  the  case  where  a  cheap  transport  line  such  as 
a  railway  or  a  navigable  river  cuts  a  more  expensive  transport  sur- 
face like  a  dense  network  of  roads. ^^°  The  angle  /?,  within  which 
transportation  to  and  from  the  railway  takes  place,  is  easily  calcu- 
lated. Since  in  this  case  AE  in  Figure  50  coincides  with  CE,  and  a 
is  therefore  90°,  sin  j3  =  fa^^  fb-  Another  application  of  the  formula 
is  the  construction  of  railway  bridges  over  broad  streams.  The 
higher  the  construction  costs  the  more  will  a  bridge  deviate  from 
the  main  direction  of  the  tracks  in  order  that  the  crossing  may  be 
made  as  short  as  possible. 

The  law  of  refraction  naturally  covers  more  difficult  cases  as  well. 
Refraction  by  lenses,  too,  has  its  counterpart  in  economics.  For  the 
solution,  it  is  completely  irrelevant  whether  the  hatched  area  in 
Fig.  51  is  a  biconcave  lens  and  the  problem  is  to  project  a  beam  of 
light  from  H  in  such  a  way  that  it  will  arrive  at  N;  or  whether  H 
is  Hawaii,  the  hatched  area  the  isthmus  of  Central  America,  and  N 
is  New  Orleans,  and  instead  of  a  beam  of  light  being  projected  a 


if  not  the  market  areas  of  man?  Plant  species  also  have  their  necessary  and  typical 
distance,  as  a  consequence  of  the  struggle  betjveen  an  individual  impulse  to  spread  and 
the  tendency  to  maximize  the  number  of  independent  existences  familiar  to  us  from 
economic  analysis.  I  doubt  that  the  fundamental  principles  of  zoological,  botanical, 
and  economic  location  theory  differ  very  greatly. 

120.  Palander  (op.  cit.,  pp.  337  ff.)  gives  an  admirable  presentation  of  the  com- 
bination of  means  of  transport.  ( (The  minimum  condition  on  the  left  side  of  the 
equation  on  p.  337,  however,  should  read  x  -^  Va^  -j-  jc^,  not  x  -j-  a) . 


i86  Part  Two.    Economic  Regions 

load  of  pineapples  is  to  be  shipped  to  New  Orleans  as  cheaply  as 
possible.  The  greater  the  refractive  index  of  the  lens— that  is,  the 
more  it  resists  the  passage  of  a  beam  of  light— the  more  will  the 
beam  be  deflected  (path  I  instead  of  path  II) ,  Exactly  so,  were 
there  no  Panama  Canal  today,  would  a  connecting  railway  be  chosen 
between  Pacific  and  Atlantic  ports  that  would  be  more  southerly 
the  higher  the  rail  tariff  in  comparison  with  the  ocean  freight.    At 


Fig.  51.  Schematic  representa- 
tion of  efficient  route  from  Hawaii 
(H)  to  New  Orleans  (N)  via  Panama 
Canal  and  possible  Nicaragua  cut 

present  the  problem  is  stated  thus:  Whether  the  cost  of  a  canal 
through  Nicaragua  would  be  repaid  by  the  shortening  of  the  sea 
voyage.  Other  things  being  equal,  the  higher  the  cost  the  shorter 
would  a  cut  have  to  be;  in  other  words,  the  greater  would  be 
the  superiority  of  the  Panama  Canal  over  one  running  through 
Nicaragua.  In  this  case  a  decision  can  be  reached  without  appeal 
to  the  law  of  refraction,  because  there  are  only  two  practical  alter- 
natives. Where  there  are  more,  which  cannot  all  be  thoroughly 
explored,  the  right  choice  can  be  made  only  with  the  help  of  this 
law. 

But  an  important  limitation  of  the  law  of  refraction  must  be 
added  here.  Its  nature  is  essentially  similar  to  Launhardt's  and 
Weber's  geometrical  figures:  it  assumes  that  the  points  between 
which  transportation  is  carried  on  are  definitely  fixed  and  few  in 
number— in  the  present  case  only  two.  Hence  the  objections  to  the 
earlier  figures  are  substantially  valid  against  the  law  in  question. 
However,  the  objections  are  less  important  here  because  transport 
lines,  with  which  we  are  now  dealing,  are  considerably  less  numerous 
than  transport  points.  In  the  case  of  ocean  traffic  between  the  east 
and  west  coasts  of  America,  for  example,  it  can  be  said,  despite  the 
numerous  harbors  and  innumerable  points  of  departure  and  arrival, 
that  in  the  neighborhood  of  the  Central  American  isthmus  at  least 
there  are  only  one  or  two  transport  lines.    But  if  the  traffic  of  the 


Some  New  Factors  ^°7 

west  coast  of  South  America  with  Europe  and  with  the  east  coast 
of  North  America  is  added,  there  will  be  several  lines,  and  for  each 
one  a  somewhat  different  situation  of  the  Panama  Canal  would  be 
more  advantageous.  Since  it  would  not  pay  to  have  a  special  canal 
for  each  transport  line  (quite  apart  from  the  fact  that  the  choice 
of  locations  is  severely  limited  for  technical  reasons) ,  the  location 
of  the  present  cut  is  a  compromise.  The  higher  the  fixed  costs  of 
overcoming  an  obstacle  to  traffic  and  the  greater  the  number  of 
transport  lines  that  have  to  surmount  it,  the  more  does  the  law  of 
refraction  lose  in  significance.  It  cannot  be  applied  to  a  group  of 
transport  lines,  that  is,  to  importing  areas.  In  such  cases,  gateways 
must  be  regarded  as  like  any  other  industrial  undertaking;  their 
location  will  be  so  chosen  as  to  reach  an  adequate  market. 

^.    Transport  Points 

Among  transport  points  the  nodal  points  are  of  special  impor- 
tance. They  are  more  favorably  situated  in  respect  to  freight  than 
mere  stopping  places.  We  have  already  seen  that  the  mechanical 
model  for  determining  the  optimum  transport  point  comes  to  rest 
only  in  them.  This  is  why  they  are  preferred  locations  for  industry 
and  trade.  Among  nodal  points  those  primarily  determined  by 
nature  (bottleneck  cities)  are  of  outstanding  importance.  Unlike 
other  nodal  points,  they  cannot  be  by-passed  by  technical  means, 
though  others  will  not  be  by-passed  for  economic  reasons.  They  are 
literally  gateways  that  must  be  passed  through.  The  particular 
barrier— a  mountain  range,  a  river,  an  unbroken  coastline— may  be 
provided  by  nature  or  may  depend  partly  on  economic  factors.  The 
expensive  means  of  transferring  goods,  say  from  a  ship  to  a  railway, 
or  of  surmounting  obstacles  (bridges,  tunnels)  presuppose  a  rela- 
tively large  supply  area,  and  thus  are  to  be  found  at  a  few  points  only. 

The  classic  example  of  a  "  pass  city  "  is  Vienna  (and  at  the  other 
end  of  a  long  curve  in  the  Danube,  Bratislava,'^^^  as  a  threefold  gate- 
way leading  into  the  Bohemian  and  Hungarian  basins,  and  into 
south  Germany.  The  narrower  the  pass  and  the  more  important 
the  market  lying  behind  this  natural  gateway,  the  nearer  to  it  will 
industries  with  large  necessary  sales  areas  establish  themselves,  other 
things  being  equal;  but  they  will  pass  through  it  only  when  there  is 
a  larger  market  on  the  other  side. 

121.  Budapest,  on  the  contrary,  is  a  gateway  not  for  river  traiBc  on  the  Danube, 
but  for  traffic  crossing  the  Danube.  (See  Blum,  *'  Deutschland  und  Siidosteuropa  nach 
Riickgliederung  der  Ostmark  und  der  Sudetenlander,  verkehrspolitisch  betrachtet," 
Zeitschrift  fiir  Verkehrswirtschajt,  XVI  [1939],  1-31;  and  Schneefuss,  in  Lebensraum- 
fragen  europdischer  Volker,  edited  by  K.  Dietzel  et  al.  [Leipzig,  1941],  p.  659.) 


jgg  Part  Two.     Economic  Regions 

A  special  problem  arises  when  the  barrier  separates  not  only 
different  markets  ^^^  but  different  means  of  transportation  as  well. 
In  such  a  case  the  pass  city  is  at  the  same  time  a  transshipment  point, 
and  if  the  pass  is  fairly  long  it  will  be  situated  as  near  as  possible 
to  the  end  where  the  more  expensive  means  of  transportation  begins. 
Hence  if  a  seaport  is  on  a  navigable  river  it  will  lie  as  far  upstream 
as  possible.^^^ 

Palander  ^-*  has  shown  how  much  larger  the  hinterland  for  a 
river  port  is  compared  with  that  for  a  seaport.  It  must  not  be 
assumed,  therefore,  that  the  choice  of  the  natural  harbor  to  be 
developed  and  the  question  of  how  far  upstream  it  shall  be  situated 
are  two  separate  problems.  It  will  not  do  to  select  a  hypothetical 
location  (in  the  wider  sense)  by  means  of  the  law  of  refraction,  say 
on  a  conventionalized  coastline  where  the  possible  seaports  have 
been  indicated,  and  then  choose  the  actual  location  (in  the  narrower 
sense)  as  far  inland  as  possible.  There  is  only  one  single  location 
problem,  and  it  cannot  be  solved  in  stages.  The  position  of  the 
hinterland,  the  destination  of  the  shipments,  the  contour  of  the 
coastline,  the  cost  of  harbor  installations,  all  must  be  considered 
simultaneously  in  a  general  calculation  that  covers  a  few  selected 
sites. 

Transport  points  play  an  important  part  in  the  formation  of 
market  areas.  If,  for  instance,  wheat  growers  supplied  wheat  con- 
sumers directly,  there  would  be  a  chaotic  plethora  of  market  areas, 
the  shape  and  situation  of  which  are  the  harder  to  imagine  because 
the  deficit  and  surplus  regions  of  wheat  are  widely  separated  geo- 
graphically. Transport  points  simplify  this  situation  so  greatly  that 
only  through  them  can  it  be  grasped.  Every  railway  station  in  a 
wheat  belt  is  a  collecting  point  in  miniature.  Each  is  surrounded 
by  its  small  supply  area,  and  the  receipts  of  each  farmer  are  equal 
to  the  uniform  unit  price  at  the  collecting  station  less  the  cost  of 
transporting  the  wheat  there.  The  nodal  traffic  points  are  the  col- 
lecting places  of  the  railway  stations.  A  larger  supply  area  surrounds 
them,  and  the  price  at  each  stopping  place  is  equal  to  that  at  the 

122.  This  holds  true  for  smaller  market  areas,  whereas  a  gateway  merely  constricts 
larger  ones.  In  general,  therefore,  countries  separated  by  mountain  chains  are  eco- 
nomically less  closely  integrated.  This  in  itself  is  a  sufficient  reason  why  Wiirttemberg 
and  Baden,  for  instance,  do  not  constitute  a  single  economic  area.  Mountains  make 
Chile  an  independent  economic  region;  her  share  in  the  foreign  trade  of  Argentina 
amounts  to  but  a  small  percentage. 

123.  This  is  especially  important  when  the  possible  supply  radius  is  not  much 
longer  than  the  necessary  one.   Furthermore,  port  installations  are  cheaper  on  a  river. 

124.  Op.  cit.,  p.  349. 


Some  New  Factors  i°9 

superior  nodal  point  less  the  freight.  The  collecting  stations  for 
these  collecting  stations,  finally,  are  the  few  great  ports  that  export 
wheat.  In  each  the  product  of  an  enormous  hinterland  is  assembled. 
Only  these  great  gateways  can  give  rise  to  great  delivery  regions  in 
place  of  the  small  supply  areas.  Furthermore,  they  simplify  the 
spatial  price  system.  All  prices  at  the  subordinate  collecting  stations 
are  determined  by  a  single  price  at  the  port  and  the  freight  to  it.^^^ 

If  this  uniform  price  falls,  the  hinterland  of  the  port  becomes 
smaller  and  more  fragmentary.  Smaller,  because  in  the  region  of 
the  farthest  nodal  points  or  "  whistle  stops  "  the  cultivation  of  wheat 
would  be  no  longer  profitable;  more  fragmentary,  because  even  in 
the  nearer  part  of  the  hinterland  individual  farmers,  who  are  espe- 
cially far  from  the  railway,  or  own  poor  soil,  or  lack  ability,  will 
now  give  up.  The  important  function  of  price  in  the  ordering  of 
spatial  relations  is  unmistakable. 

The  sales  area  for  wheat  is  simplified  in  like  manner.  To  be 
sure,  simplification  does  not  go  so  far  that  only  one  exporting  port 
for  wheat  in  the  whole  world  supplies  one  single  importing  port. 
In  such  a  case  everything  would  be  perfectly  clear:  one  single  area 
would  be  confronted  with  one  single  supply  area  and  there  would 
be  a  single  world  price  for  wheat,  which  could  be  chosen  at  either 
the  export  or  the  import  harbor,  since  it  would  differ  only  by  the 
freight. 

But  it  is  not  quite  so  simple  in  reality.^^®  Even  if  we  neglect 
the  product  that  is  locally  consumed,  several  supply  areas  are  related 
to  several  consuming  areas.   Almost  every  exporting  port  ships  to 

125.  When  wheat  is  traded  between  places,  local  prices  differ  exactly  by  the  cost 
of  shipment;  otherwise  they  may  differ  by  less.  In  such  cases  considerable  local  price 
variations  may  exist  without  any  movement  of  goods.  If  A  and  B  supply  C,  the  price 
in  A  may  be  above  or  below  that  in  B  by  as  much  as  the  freight,  and  yet  no  trade 
will  take  place  between  them.  This  does  not  mean  that  the  difference  can  fluctuate 
within  these  limits  as  long  as  A  and  B  have  a  surplus.  Since  price  fluctuations  always 
originate  at  the  central  collecting  station,  they  must  be  exactly  the  same  for  all  sub- 
ordinate places.  Gateway  points  fix  spatial  price  differences  rigidly,  for  permanent 
surplus  as  well  as  for  permanent  deficit  places.  Prices  in  A  and  B  always  differ, 
therefore,  by  the  difference  in  freight  from  y4  to  C  or  from  B  to  C.  Otherwise  one  of 
the  two  places  would  be  excluded  as  a  source  of  supply.  Only  when  A  and  B  supply 
two  different  and  unconnected  places  can  the  price  in  A  be  higher  or  lower  than  that 
in  B  by  almost  the  amount  of  the  freight  to  B,  and  vary  arbitrarily  within  these  limits, 
without  one  of  the  places  being  driven  entirely  from  the  market.  The  actual  frequency 
of  fluctuations  in  the  price  differences  between  two  places  is  due  not  only  to  frictional 
difficulties,  but  also  partly  to  slight  product  differences  and  partly  to  the  fact  that 
many  places  sometimes  have  a  surplus  and  sometimes  a  deficit. 

126.  See  the  section  on  the  "  World  Market "  in  Chapter  23,  b,  §4. 


igo  Part  Two.    Economic  Regions 

several  importing  ones,  and  almost  every  importing  one  receives  from 
several  exporting  ports.  This  is  an  unusual  situation.  We  should 
expect  several  consumers  to  order  from  one  producer,  or  several 
producers  to  supply  one  large  consumer.  Does  this  strange  over- 
lapping of  areas,  as  it  is  found,  for  example,  in  the  wheat  market, 
depend  solely  upon  differences  in  the  product,  or  can  it  be  explained 
in  some  other  way? 

Suppose  the  prices  in  all  ports  of  exportation  to  be  given.  Then 
in  principle  a  small  importing  port  can  obtain  wheat  of  the  same 
quality  from  only  one  exporting  port,  for  only  to  the  few  importing 
ports  on  the  borders  of  the  sales  areas  of  two  exporting  ports  is  it  a 
matter  of  indifference  whether  they  supply  the  one  or  the  other,  or 
both.  But  suppose  that  the  import  needs  of  one  of  these  border 
ports  are  very  great,  and  cannot  be  met  at  all  by  a  single  exporting 
port,  or  only  when  the  import  price  rises.    Such  an  importing  port 


Fig.  52.  Effect  of  gate  cities  on  market  and  supply  areas.  A,  B,  C, 
and  D  are  export  ports  with  separate  sales  areas.  £  is  a  large  importing 
port,  whose  supply  area  is  endorsed  by  a  broken  line. 

(Liverpool,  for  example)  is  not  only  a  border  point  for  the  sales 
areas  of  several  ports,  but  at  the  same  time  the  center  of  a  supply 
region  on  whose  borders  lie  those  exporting  ports  that,  among  others, 
supply  the  great  importing  port.  The  same  exporting  ports  can 
supply  in  common  only  such  importing  ports  as  lie  on  their  common 
boundary.  But  it  seldom  happens  that  more  than  two  sellers  share 
more  than  a  corner  of  their  sales  areas. 

With  these  considerations  we  have  shown  an  important  and 
remarkable  effect  of  the  gateway  points:  They  can  of  themselves 
create  a  state  of  imperfect  competition  between  millions  of  inde- 
pendent producers  and  millions  of  independent  consumers.  This  is 
expressed  by  the  fact  that  to  large  buyers  on  a  border  it  is  not  a 
matter  of  indifference  (as  it  is  to  small  buyers)  how  much  they  buy 
from  each  sales  center  on  the  border  of  whose  areas  they  lie.  As  an 
example,  England  and  Peru  buy  wheat  from  Canada,  the  United 


Some  New  Factors  191 

States,  Argentina,  and  Australia.  But  whereas  it  would  make  little 
difference  if  Peru  were  to  get  its  entire  supply  from  Argentina,  the 
whole  spatial  price  structure  would  be  radically  altered  if  England 
were  to  try  the  same  thing.  For  England  buys  over- a  third,  Peru 
only  an  insignificant  fraction,  of  the  combined  amounts  exported 
by  the  countries  mentioned.  The  share  of  the  various  surplus  regions 
in  English  imports  is  uniquely  determined  in  equilibrium. 

Thus  the  characteristic  effect  of  gateway  points  is  twofold.  First, 
they  create  a  few  great  supply  and  sales  areas.  Second,  when  one  or 
another  of  these  turns  out  to  be  especially  large  they  cause  a  strange 
overlapping.  With  a  standardized  product,  however,  the  sales  areas 
will  only  touch,  but  supply  and  sales  areas  will  in  this  case  over- 
lap!   (Fig.  52.) 

c.     HUMAN    DIFFERENCES 
§1.     Differences    among   Individual   Entrepreneurs 

As  the  planning  curve  of  a  less  capable  entrepreneur  lies  above 
that  of  an  abler  one,  the  necessary  extent  of  his  sales  area  and  his 
producer's  price  are  generally  greater,  which  can  easily  be  deduced 
from  a  graph.  The  unskillful  one  could  not  maintain  himself  if 
there  were  enough  capable  ones.  This  is  probably  true  in  old 
established  trades,  because  in  order  to  succeed  the  head  of  an  enter- 
prise need  only  good  average  abilities  such  as  approach  those  most 
often  found,  since  human  characteristics  seem  to  be  distributed 
along  the  Gaussian  frequency  curve.  Very  good  and  very  bad  entre- 
preneurs should  be  relatively  uncommon  in  these  branches,  and  the 
regional  size  should  be  about  equal. 

In  pioneer  industries,  however,  where  a  rather  infrequent  com- 
bination of  characteristics  is  required,  less  able  entrepreneurs  may 
also  find  a  place,  though  they  are  still  above  average.  Will  the  abler 
producers  be  content  with  small  sales  areas  and  leave  large  markets 
to  the  less  skillful,  who  could  not  otherwise  exist?  The  outcome  is 
as  though  all  entrepreneurs  were  competing  in  the  same  market: 
The  well  qualified  extend  their  sales  areas  until  at  the  boundaries, 
which  now  extend  farther  outward  than  need  be,  the  price  is  equal 
to  that  at  the  boundaries  of  the  necessary  sales  areas  of  their  less 
skillful  neighbors.  Consequently  the  actual,  though  not  the  neces- 
sary, sales  areas  of  the  ablest  will  be  larger  than  those  of  the  others.^" 

127.  As  the  capabilities  of  a  leading  entrepreneur  can  extend  his  sales  area  in 
general,  so  the  special  abilities  of  his  regional  sales  representative  can  expand  it 
greatly  in  a  certain  direction. 


192 


Part  Two.     Economic  Resions 


In  a  literal  sense  they  are  the  ones  with  the  larger  sphere  of  influence. 
Since  they  prefer  great  cities  as  locations  wherever  possible,  their 
sales  areas  will  be  often,  and  perhaps  usually,  above  the  average  in 
size  for  this  reason  alone. 

§2.     Differences    in    National   Character 

The  character  of  a  people  expresses  itself  also  in  the  way  in 
which  they  organize  their  economic  life.  But  such  national  differ- 
ences interest  us  here  only  in  so  far  as  they  operate  spatially— which 
presupposes  that  the  various  races  and  nationalities  are  not  thor- 
oughly intermixed.  Where  consumption  is  still  rigidly  determined 
by  a  common  way  of  life  (that  is,  where  it  represents  a  meaningful 
group  of  needs  similar  for  all),  tribal,  national,  and  racial  differences, 
like  all  differences  between  regionally  confined  groups,  are  of  great 
economic  importance  from  a  spatial  standpoint.  Then  the  boundaries 
of  a  tribe  or  nation  are  at  the  same  time  the  boundaries  of  regional 
networks  for  whole  classes  of  goods.  Not  much  is  altered  when  in 
cosmopolitan  periods  customs  and  usages  relax  and  become  more 
similar.  But  even  when  they  do,  and  advertising  and  fashions  of  the 
day  instead  of  established  custom  attempt  to  determine  consumption, 
not  all  boundaries  are  obliterated.  Many  customs  are  determined  by 
the  character  of  a  landscape,  by  its  history,  and  perhaps  biologically 
too,^^^  and  can  be  changed  only  slowly  or  not  at  all.^^^  Thus  a  native 
born  entrepreneur  can  judge  more  accurately  what  compromise 
with  the  prevailing  fashion  will  be  possible.  His  solution  and  his 
advertising  will  correspond  more  closely  with  the  national  or  tribal 
character,  and  up  to  a  certain  point  national  boundaries  will  still 
remain  economic  boundaries. 

128.  Heredity  and  landscape  affect  national  character  in  part  directly,  in  part 
through  tradition,  which  also  is  largely  determined  by  historical  chance.  For  the 
influence  of  landscape  see  W.  Hellpach,  Geopsyche   (5th  ed.,  1939) . 

129.  Conversely,  one  of  the  most  striking  phenomena  to  a  European  visiting  the 
United  States  is  how  little  its  great  regional  differences  have  been  transmuted  into 
differences  in  character  and  custom,  and  hence  in  consumption,  even  though  the  subtle 
variations  are  greater  than  appears  at  first  sight.  One  gets  the  impression  that  the 
American  is  nature's  master  and  shapes  it,  rather  than  allowing  it  to  shape  him.  This 
imposing  uniformity  (as  Ratzel  has  put  it)  is  one  of  the  sources  of  America's  wealth. 
If  there  were  as  many  cultural  differences  there  within  the  same  space  as  in  Europe, 
cheap  mass  production  would  be  finished.  Earnings  at  least  would  fall,  though  psychic 
income  need  not.  Incidentally,  it  is  just  this  economic  and  cultural  uniformity  that 
makes  the  strong  political  position  of  the  individual  states  so  little  dangerous  to  the 
Federal  Government.  Nevertheless,  even  in  the  United  States  the  heyday  of  the 
regional  is  only  beginning. 


So7ne  New  Factors  193 

But  production,  too,  is  largely  influenced  by  the  individuality  of 
producers,  even  when  they  do  not  work  exclusively  for  their  own 
needs.  What  is  produced  will  naturally  depend  in  great  measure 
upon  the  special  skill  of  a  people,  though  it  cannot  be  said  simply 
that  they  will  produce  that  which  relatively  they  know  best.^^° 

Characteristic  skills  must  not  be  invariably  regarded  as  given 
a  priori,  since,  for  example,  they  often  require  a  suitable  task  for 
their  development.  Thus  the  parsimony  of  nature  will  spur  some 
peoples  on,  but  discourge  others.  It  is  by  no  means  objective 
criteria  alone  that  decide  what  a  location  is  suitable  for,  since 
different  peoples  will  develop  it  differently.  They  react  differently 
to  their  human,  as  they  do  to  their  natural,  environment.  The 
diversity  of  production  of  a  people  is  determined  by  how  far  they 
can  resist  a  general  leveling.  The  more  they  can  do  so,  the  less 
will  they  specialize  one-sidedly  in  goods  for  a  larger  market.^^^ 
They  will  neither  simply  accommodate  themselves  to  an  unfamiliar 
demand  nor  be  satisfied  with  goods  that  are  fashionable  elsewhere.^^^ 
Such  loyalty  to  the  native  and  indigenous  has  enormous  advantages, 

130.  For  further  details  see  pp.  226  ff.  and  236  ff.  Ability  varies  among  the  citizens 
of  different  places,  especially  among  those  of  larger  and  smaller  towns.  The  former 
often  work  faster,  the  latter  better. 

131.  The  real  meaning  of  European  colonial  policy  was  chiefly  to  enforce  speciali- 
zation. 

132.  It  is  hardly  possible  to  overestimate  the  degree  to  which  a  too  sudden  or  too 
great  concentration  of  production  may  uproot  an  established  way  of  life,  or  how  trade 
may  alienate  a  people  from  their  soil.  Foreign  in  place  of  domestic  wood  in  the  con- 
struction of  furniture,  fruit  that  has  never  been  seen  to  ripen,  clothing  that  might  do 
for  a  different  climate,  travel  among  cultural  surroundings  for  which  one  is  not 
prepared,  a  thousand  things  that  are  possible  against  the  background  of  a  cosmopolitan 
attitude— when  all  this  suddenly  breaks  into  the  life  of  a  people,  it  is  difficult  to 
judge  calmly  which  of  the  new  economic  possibilities  will  suit  it.  For  there  is  little 
sense  in  ordering  a  multitude  of  goods  from  afar  simply  because  they  are  cheaper  or 
more  attractive,  as  long  as  one  has  not  found  in  some  way  or  other  a  place  in  one's 
world  pattern  for  their  individuality,  their  origin,  and  their  producer.  One's  horizon 
must  widen  with  the  expansion  of  markets.  But  it  would  be  far  from  right  to  hold 
that  this  expansion  of  markets  intrudes  upon  a  people  like  fate  from  without.  They 
themselves  decide  whether  it  shall  take  place  at  all;  it  depends  on  them  whether  they 
are  ready  for  it. 

Of  course  it  would  be  as  fallacious  to  prevent  the  concentration  of  production  as 
to  hasten  it.  The  enormous  increase  in  our  wealth  since  the  dawn  of  capitalism  was 
only  possible  because  we  were  willing,  on  the  whole,  to  accept  standardized  products 
instead  of  individual  ones.  America  went  further  in  this  respect,  and  that  is  one 
reason  why  she  has  more  goods.  For  Europe  there  lies  dormant  a  great  and  dangerous 
possibility  of  quickly  becoming  rich  again  after  the  war,  even  though  only  on  the 
surface. 


,Q^  Part  Two.     Economic  Regions 

far  transcending  the  diminution  in  economic  risk,"^  for  it  is  con- 
ducive to  a  more  harmonius  development  of  human  nature.  The 
individual  will  have  to  specialize  everywhere,  but  it  makes  a  great 
difference  whether  in  his  sphere  "*  there  are  only  associates  who 
specialize  in  the  same  field,  or  whether  he  is  surrounded  by  men 
who  live  for  him  the  other  possibilities  that  he  has  had  to  forego- 
that  is,  whether  his  horizon  constitutes  a  complete  whole. ^^^ 

Tribal  and  national  characteristics  show  also  in  the  conduct  of 
business.  There  is  not  nearly  enough  attention  paid  to  how  much 
not  only  individuals,  but  tribes  and  nations  ^^®  as  well,  vary  in  such 
characteristics  as  timidity  or  daring,  discretion  or  rashness,  a  liking 
for  tradition  or  for  innovation,  a  conservative  or  a  flexible  mind, 
thorough  or  superficial  training,  stability  or  frivolity,  and  to  how 
strongly  these  differences  dominate  the  character  of  their  economies: 
the  objects  produced,  the  size  of  their  undertakings,  the  relation 
between  an  entrepreneur  and  his  workers,  the  mobility  of  labor 
and  capital,  the  strategy  of  monopolists,  location,  resistance  to  crises, 
and  so  on.  All  these  depend  not  only  upon  the  individual  entre- 
preneur, but  also  upon  the  environment  in  which  he  works  as  well 
as  upon  his  environment  in  a  spatial  sense,  since  the  intimacy  of 
economic  relations  generally  decreases  with  distance. 

When  an  explanation  was  sought  for  the  fact  that  the  economy 
of  Wiirttemberg  withstood  the  great  depression  of  the  'thirties 
especially  well,  the  discussion  occasionally  touched  upon  these 
matters.  But  many  explanations  did  not  get  near  enough  to  the 
root  of  the  matter.  The  poverty  of  the  region  in  natural  raw 
materials  was  certainly  a  piece  of  good  fortune  in  this  instance. 
But  the  balance  of  the  economic  structure,  as  shown  in  the  diversity 
of  production  and  particularly  in  the  happy  combination  of  industry 
and  agriculture,  and  again  in  the  dispersion  of  industry  and  landed 

133.  The  expansion  of  markets  gained  at  the  price  of  specialization  also  tends  to 
diminish  risks  (see  E.  Willeke,  Von  der  raumgebundenen  menschlichen  Arbeitskraft 
[Jena,  1937],  p.  113),  but  this  rarely  suffices  to  compensate  for  the  increased  risk  con- 
nected with  specialization  itself. 

134.  This  broadens  with  improvements  in  transportation,  though  not  necessarily  at 
the  same  rate. 

135.  For  the  development  of  a  cultural  individuality  a  landscape  must  therefore  be 
large  enough  to  constitute  a  world  in  miniature,  yet  at  the  same  time  small  enough 
to  be  more  or  less  understood  by  its  intellectual  leaders. 

136.  For  national  types  of  entrepreneurs  see  W.  Sombart,  Der  Bourgeois  (Munich, 
1913),  pp.  170-193,  266-281);  K.  Wiedenfeld,  Das  Personliche  im  modernen  Unter- 
nehmertum  (Leipzig,  1920)  ;  and  R.  Michels,  Wirtschaft  und  Rasse.  Grundriss  der 
Sozialokonomik   (2d  ed.,  1923) ,  Vol.  II,  Pt.  1. 


Some  New  Factors  .  195 

property  ^"  resulting  from  free  divisibility  and  deliberate  policy  ^^*— 
these  were  not  due  to  chance.  Whoever  considers  thoroughly  the 
particular  nature  of  the  products  and  production;  the  highly  valu- 
able specialties  that  can  be  made  only  by  unusually  well-trained 
and  adaptable  workers  who  like  to  tinker  and  experiment;  whoever 
considers  the  energetic  yet  sound  business  policy  that  clings  to  easily 
understood  and  controlled  conditions  and  to  enterprises  seldom 
exceeding  the  capital  and  labor  resources  of  one  family  ^^^  (just  as 
Wiirttemberg  itself  in  many  respects  resembles  a  large  family  which 
has  contributed  greatly  to  the  easing  of  social  tension  and  encouraged 
the  use  of  native  products)  —whoever  considers  all  these  factors  will 
see  clearly  that  national  character  has  influenced  this  economy  to 

137.  Well  described  by  G.  Stockmann,  "  Grundlagen  und  Krisenfestigkeit  der 
wiirttembergischen  Industrie,"  Deutsche  Zeitschrift  fiir  Wirtschaftskunde,  I  (1936) , 
281-298.  See  also  the  great  atlas  of  P.  Hesse  et  al.,  Landvolk  und  Landwirtschaft  in 
den  Gemeinden  von  Wurttemberg-Hohenzollern  [Kartenwerk)  (Stuttgart,  1939);  and 
several  contributions  in  Weltwirtschaft,  1934,  No.  11/2. 

138.  Ever  since  1848  the  Zentralstelle  fiir  Gewerbe  und  Handel  (the  present  Landes- 
gewerbeamt)  fulfilled  certain  functions  of  a  regional  planning  office  in  an  exemplary 
manner,  more  recently  under  the  farsighted  leadership  of  Ferdinand  von  Steinbei' 

139.  According  to  233  official  American  studies,  the  largest  enterprises  are  seldom 
the  cheapest;  it  is  generally  the  medium-sized  and  often  the  small  ones  (G.  J.  Stigler, 
American  Economic  Review,  June,  1942,  Pt.  2) .  As  for  agriculture  in  Wiirttemberg, 
the  number  of  farms  that  are  too  small  is  apt  to  be  overestimated  (see  above,  p.  65, 
note  53)  .  The  net  market  return  (money  receipts  less  expenses)  in  1934  amounted 
in  Baden  to  155  reichsmarks  per  hectare,  in  Wiirttemberg  to  145,  in  Hanover  to  124, 
in  Schleswig-Holstein  to  88,  and  in  Pomerania  to  73.  Large  farms  were  more  common 
and  most  natural  yields  larger  in  the  same  order,  but  this  was  achieved  by  a  greater 
outlay  for  machinery  and  artificial  fertilizers.  "  The  economic  efficiency  of  an  area 
under  cultivation  increases  as  its  size  decreases."  (H.  Priebe,  "  Zur  Frage  der  Gestaltung 
und  Grosse  des  zukiinftigen  bauerlichen  Familienbetriebes  in  Deutschland,"  Berichte 
iiber  Landwirtschaft,  Neue  Folge,  XXVII  [1942],  585.)  Though  higher  money  return 
per  hectare  does  not  entirely  compensate  for  the  thicker  settlement  of  regions  containing 
small  farms  (the  net  return  per  person  principally  engaged  in  agriculture  was  300 
reichsmarks  in  Wiirttemberg  and  400  in  Pomerania)  ,  the  difference  almost  vanishes 
when  it  is  taken  into  account  that  on  a  peasant  farm  an  especially  large  number  of 
workers  are  employed,  such   as   children   or  old   people,  who  are  not   fully  efiBcient. 

(G.  Isenberg,  "  Die  Tragfahigkeit  des  deutschen  Ostens  an  landwirtschaftlicher  und 
gewerblicher  Bevolkerung,"  in  Struktur  und  Gestaltung  der  zentralen  Orte  des  deutschen 
Ostens  [Leipzig,  1941],  p.  13.) 

In  any  case,  depopulation  of  the  Swabian  villages  would  affect  the  vitality  of  industry 
itself  through  the  loss  of  the  qualitatively  irreplaceable  younger  generation  (Bosch 
himself,  typical  in  so  many  ways,  came  as  a  peasant  boy  from  the  Swabian  Alps)  and 
would  altogether  sap  the  energy  of  the  whole  region,  which  springs  psychically  and 
economically  from  the  fertile  proximity  of  man  and  nature.  Even  without  such  a 
depopulation  much  is  taking  place  in  Wurttemberg  that  some  day  may  change  favor- 
able into  unfavorable  conditions. 


!<)()  Part   Two.     Economic  Regions 

an  extraordinarily  high  degree. ^*°  The  Swabian  economy  cannot  be 
entirely  grasped  without  an  understanding  of  Swabian  philosophy, 
which  has  probably  formulated  this  national  character  in  the  most 

apt  way.^*^ 

d.     POLITICAL    DIFFERENCES 

Countries  and  economic  regions  do  not  necessarily  coincide.  It 
lies  with  the  state  as  an  independently  governed  society,  and  hence 
in  the  final  analysis  with  the  people  themselves,  whether  or  not  it 
shall  be  entirely  self-sufficient  economically;  that  is,  whether  its 
outer  economic  boundaries  shall  coincide  with  its  political  boun- 
daries, or  whether  deliberate  state  interference  shall  remain  limited 
to  arranging  the  economy  in  such  a  way  that,  once  set  going,  it  shall 
continue  on  the  whole  by  itself.^*^  In  the  latter  case  many  economic 
boundaries  will  extend  beyond  its  frontiers.  Between  these  two 
clear-cut  extremes  there  is  naturally  an  infinite  variety  of  less  well 
defined  economic  policies,^*^  but  we  shall  limit  the  following  para- 
graphs chiefly  to  the  second  limiting  case,  because  it  allows  recog- 
nition of  the  minimum  extent  of  political  influences  on  the 
formation  of  economic  areas.  The  discussion  will  be  preceded  by  a 
comparison  between  purely  political  and  purely  economic  regions. 

§1,     States  and  Economic  Landscapes:    A  Comparison 

a.    Similarities 

1.  States  and  economic  landscapes  each  have  a  capital  toward 
which  their  subdivisions  and  main  traffic  routes  are  oriented.^** 

2.  Both  kinds  of  capital  are  located  as  centrally  as  possible, 

140.  E.  Preiser  (Die  Wiirttembergischer  Wirtschaft  ah  Vorbild  [Stuttgart,  1937], 
p.  79)  justly  praises  it  for  having  disarmed  the  most  damagaing  criticism  of  capitalism 
by  its  relative  invulnerability  to  crises,  its  spatial  arrangement,  and  its  social  harmony. 

141.  See  H.  O.  Burger,  Schwabentum  in  der  Geistesgeschichte  (Stuttgart,  1933)  . 

142.  It  is  not  quite  accurate  to  speak  of  rules  of  the  economic  game  set  up  by  a 
state.  For  in  the  economy  the  individual  (though  not  all  individuals  together)  can  do 
about  as  he  pleases  without  disturbing  its  functioning,  which  is  not  true  of  a  game. 
A  free  economy  is  rather  constructed  precisely  in  such  a  manner  that  it  functions  as  a 
whole,  no  matter  what  the  individual  may  do.  The  most  important  exception  to  this 
statement  concern  monopolistic  tendencies,  which  must  therefore  be  supervised  or 
checked. 

143.  Thus  it  is  only  a  question  of  convenience  whether  to  regard  free  trade  as  normal 
and  state  interference  as  a  disturbance,  or  to  begin  with  state  planning  and  show  the 
workings  of  economic  forces  within  this  given  framework.  Similarly,  the  actual  inter- 
mediate condition  may  be  derived  from  either  free  competition  or  monopoly. 

144.  This  explains  the  odd  fact  that  frontiers  of  the  German  states  are  often  language 
boundaries  without  being  tribal  boundaries.  The  border  between  Bavaria  and  Wiirt- 
temberg  is  an  example.   The  Swabians  just  over  the  line  speak  a  dialect  tinctured  with 


Some  New  Factors  197 

taking  into  consideration  the  location  of  competitors  and  the  fact 
that  tlieir  functions  are  not  demanded  in  a  uniform  manner  through- 
out the  whole  area  and  that  local  locational  advantages  are  not 
everywhere  the  same. 

3.  The  tendency  toward  equal  size  is  common  to  both  states 
and  economic  landscapes.  This  we  have  already  shown  for  economic 
areas.  For  states  the  reader  is  referred  to  Ratzel,  who,  in  his  great 
Politische  Geographie,  ascribes  to  the  notion  of  equilibrium  the 
fact  that  neighboring  states  in  competition  with  one  another  struggle 
toward  equal  size.^*^  In  this  mutual  pressure  and  thrust  the  pecu- 
liarities of  the  central  position  are  the  same  in  both  cases;  it  is  as 
powerful  in  strength  as  it  is  threatened  in  weakness. ^*^ 

4.  The  size  of  states  and  economic  landscapes,  of  administrative 
districts  and  market  areas,  depends  in  great  measure  on  the  develop- 
ment of  transportation  and  production  techniques.  In  every  case 
the  size  must  be  at  least  such  as  to  assure  existence;  that  of  economic 
landscapes  and  market  areas  through  markets,  that  of  states  and 
administrative  districts  through  po'^ver.  If  they  exceed  this  size 
there  arise  the  rich  entrepreneur  and  the  mighty  state.  The  former 
can  afford  to  be  generous,  the  latter  magnanimous. 

5.  The  boundaries  of  states  and  economic  landscapes  cut  through 
regular  market  networks,  which  results  in  economic  losses. 

6.  Boundaries  have  the  function  of  separating  the  various  orders. 
Enclaves  and  exclaves  are  politically  and  economically  unprofitable. 

7.  The  influence  of  centers  always  grows  less  toward  the  peri- 
phery. The  capitals  and  their  immediate  surroundings  differ  more 
sharply  from  each  other  than  do  the  border  regions.  Just  as  we 
have  seen  market  areas  on  the  borders  of  economic  landscapes  that 
did  not  belong  exclusively  to  either  of  the  adjoining  orders,  and 
just  as  the  border  zones  of  individual  market  areas  are  most  easily 
lost  to  competitors,  so  a  political  boundary  region  is  most  endan- 
gered. Furthermore,  administrations  on  either  side  of  a  frontier 
co-operate  in  many  ways  (joint  river  commissions,  for  example)  ; 
there  are  sundry  overlaps,  such  as  customs  exemptions;  and  diverse 
privileges  granted  to  the  neighbor  state,  as  when  the  border-control 
formalities  are  performed  in  the  neighboring  country's  frontier 
station    (see  Ratzel,  op.  cit.,  p.  487) . 


Bavarian  because  they  are  oriented  toward  Munich  both  politically  and  culturally;  this 
is  especially  true  of  teachers  and  clergymen,  who  are  so  important  in  the  evolution  of 
a  language. 

145.  F.  Ratzel,  Politische  Geographie    (Munich,  1897),  p.  221. 

146.  Ibid.,  p.  282. 


jqg  Part  Two.     Economic  Regions 

Thus  political  and  economic  areas  have  their  most  important 
principles  of  organization  as  well  as  many  properties  in  common. 
Because  of  this  structural  similarity  it  is  no  wonder  that  states  and 
economic  regions  frequently  overlap;  at  least  in  the  sense  that  their 
political  and  economic  capitals  coincide,  that  political  boundaries 
are  at  the  same  time  boundaries  of  many  market  areas,  and  that 
many  market  areas  and  administrative  districts,  or  at  least  their 
capitals,  are  identical. 

/3.    Dissimilarities 

1.  Political  frontiers  are  more  rigid  than  economic  boundaries. 
They  are  not  so  easily  changed. 

2.  Political  frontiers  are  wider,  so  to  speak,  than  economic  boun- 
daries. States,  like  oases,  are  separated  as  in  a  great  desert  by 
customs  duties,  laws,  language,  a  sense  of  community,  insecurity,^*'^ 
and  destiny.  Economic  boundaries  separate  only  through  minute 
price  differences. 

3.  Political  frontiers  are  more  sharply  defined  than  economic 
boundaries.  To  be  sure  political  boundaries,  too,  may  be  belts 
rather  than  lines,"^  particularly  when  they  depend  upon  natural 
features.  But  the  influence  of  the  center  grows  less  toward  the 
border  in  both  cases.  Nevertheless,  the  overlaps  and  transitions  are 
disproportionately  more  common  in  economic  landscape  boundaries. 
There  are  profound  reasons  for  this.  On  economic  boundaries  there 
live  individuals,  small  units  that  make  a  gradual  transition  possible 
and  are  at  the  same  time  concrete  units  that  "  collide  in  space  "  and 
to  whom  distance  therefore  means  something.  On  political  frontiers 
two  organizations  meet,  and  often  two  nations— large  and  in  certain 
respects  abstract  units,  for  whom  distance  changes  little  or  nothing. 
It  has  been  truly  said  that  patriotism  draws  no  distinctions  within, 
but  sharp  limits  without. "^^^'°  Economic  boundaries  change  as  profit 
changes.    With  political  boundaries,  ideas  or  the  people  change,  or 

147.  Especially  since  the  two  political  principles  that  are  so  important  to  world 
trade— balance  of  power  and  differentiation  between  war  and  peace— were  abandoned 
after  World  War  I.  (See  W.  Euken,  "  Staatliche  Strukturwandlungen  und  die  Krisis 
des  Kapitalismus,"  WeltzvirtschaftUches  Archiv,  XXXVI  [1932.],  297-321,  particularly 
p.  309.) 

148.  See  Ratzel,  op.  cit.,  p.  451;  and  J.  Solch,  Die  Auffassung  der  "  natiirlichen 
Grenzen  "  in  der  wissenschaftlichen  Geographic    (Innsbruck,  1924) ,  p.  26. 

149.  W.  Sulzbach,  Rationales  Gemeinschaftsgefiihl  und  wirtschaftliches  Interesse 
(Leipzig,  1929) . 

150.  Thus  List's  program  was  an  eminently  patriotic  one:  railroads  in  the  interior, 
and  tariffs  at  the  border  to  protect  infant  industries. 


Some  New  Factors  199 

at  least  the  organization  for  the  sake  of  which  the  individual  sacrifices 
something.  Hence  economic  ties  are  very  much  looser  and  weaker 
than  political  ties.  Between  economic  landscapes  transitional  areas 
are  possible  which  derive  no  advantages  from  definite  orientation 
toward  one  or  another  order.  Between  states,  on  the  contrary,  the 
individual  must  choose. 

4.  The  goals  of  economic  landscapes  and  states  are  different.  If 
those  for  states  are  arranged  in  a  descending  order  as  follows:  con- 
tinuance, power,  Kultur,  prosperity,  this  order  must  be  exactly 
reversed  for  economic  areas.  Entirely  different  sides  of  human 
nature  are  expressed  in  the  political  and  economic  orders. 

y.    Political  and  Economic  Boundaries 

In  certain  respects  the  boundaries  of  economic  landscapes  have 
exactly  the  same  effect  as  political  frontiers,  even  though  the  two 
are  of  opposite  nature.  The  former  resemble  a  seam,  the  latter  a 
cut,  through  the  elaborate  maze  of  market  networks.  Both  have  the 
same  effect,  however.  Both  break  up  the  regular  meshes,  which  are 
then  replaced  by  relatively  uneconomic  types  of  areas.  In  order  to 
minimize  this  disadvantage  there  is  a  tendency  to  reduce  the  length 
of  boundaries,  first  by  making  political  and  economic  boundaries 
coincide  wherever  possible,  and  second  by  making  states  and  eco- 
nomic landscapes  as  large  as  possible.  Fewer  economic  landscapes 
may  be  able  to  maintain  themselves  within  a  given  area,  therefore, 
than  if  there  were  no  frictions  at  the  boundary. 

On  both  types  of  boundary  the  regular  areal  network  shows  gaps, 
which  are  filled  in  by  irregular  areal  forms.  In  other  respects,  how- 
ever, the  two  situations  are  as  different  as  those  of  two  men  with 
entirely  different  starting  points  and  destinations  who  meet  along 
the  way.  On  economic  landscape  boundaries  the  tendency  prevails 
to  close  unavoidable  gaps  wherever  possible;  on  state  frontiers,  to 
open  avoidable  gaps  wherever  possible.  It  is  characteristic  of  eco- 
nomic landscape  boundaries  that  they  offer  a  particularly  favorable 
location  for  the  centers  of  market  areas  that  fill  in  these  gaps  and 
thus  extend  across  the  boundary.  It  is  characteristic  of  state  frontiers, 
on  the  contrary,  to  hamper  the  crossing  of  boundaries  by  market 
areas  (that  is,  the  filling  in  of  gaps) ;  to  create  new  gaps  in  a  market 
network  where  none   exist  ^"    (for  a  boundary  can  pass  directly 

151.  In  the  extreme  case  a  whole  state  is  cut  out  of  the  market  area  to  which  it 
belongs  because  of  its  situation.  The  entire  state  becomes  a  market  by  itself,  an 
artificial  gap,  whose  existence  is  assured  by  protective  tariffs  and  made  profitable  by 
a  national  industry  that  prospers  in  their  shadow. 


200  Part   Two.     Economic  Regions 

through  an  economic  landscape)  ;  and  with  certain  exceptions  to 
discourage  industries  from  settling  near  a  boundary,  where  in  fact 
they  often  have  a  market  in  one  direction  only. 

This  explains,  too,  why  after  a  shifting  of  political  frontiers  the 
new  border  regions  so  often  become  depressed  areas.  Not  only  must 
they  transpose  their  economic  activities;  they  must  curtail  them  as 
well.  This  devastating  effect  of  boundaries  would  be  still  more 
apparent  if  they  did  not  so  often  pass  through  regions  that  would 
be  thinly  settled  in  any  case  (such  as  mountainous  frontiers) ,  or 
through  regions  (such  as  those  along  river  boundaries)  that  by 
nature  are  especially  thickly  settled,  so  that  the  population  density 
in  the  latter  case  appears  normal  anyway  and  in  the  former  is 
attributed  to  the  parsimony  of  nature  alone.  But  when  a  boundary 
opens  up  gaps  and  keeps  them  open— that  is  to  say,  prevents  their 
closure  by  industrial  enterprises  on  the  boundary— the  result,  so  far 
as  no  multiplication  of  the  interior  market  can  be  achieved  by 
regrouping  (which  is  also  relatively  uneconomic) ,  is  greater  excess 
profits  but  almost  always  a  poorer  supply  for  the  consumer. 

Why  do  political  boundaries  exert  this  effect?  The  secondary 
phenomena  that  are  usually  associated  with  them  are  to  blame. 
First,  they  are  almost  always  customs  boundaries  as  well.  But  tariffs 
are  like  rivers,  which  separate  their  banks  economically  more  than 
would  correspond  to  their  actual  width. ^^^  Second,  they  are  often 
national  frontiers  also.  Differences  in  language,  in  requirements, 
and  in  national  character  have  the  same  effect  as  customs  duties. 
Third,  they  are  administrative  boundaries,  which  means  on  the  one 
hand  that  public  contracts  are  only  reluctantly  awarded  beyond  the 
border,  and  on  the  other  that  business  traffic,  to  the  extent  that  it 
is  associated  with  official  traffic,  as  is  especially  common  among 
country  folk,  does  not  cross  the  border.  Fourth,  border  regions  are 
regions  of  danger,  for  special  consideration  must  be  given  to  military 
requirements  even  in  time  of  peace,  and  in  war  they  are  the  most 
seriously  threatened  areas. 

§2.     Economic   Areas   as   Basis   for  the   State 

We  shall  begin  our  investigation  by  sketching  at  least  the  influ- 
ence of  an  economic  area  on  the  state,  and  conclude  with  a  more 
minute  analysis  of  the  inverse  relationship.   It  need  hardly  be  men- 

152.  Thus  tariffs  are  equivalent  to  a  lengthening  of  transport  routes.  The  length- 
ening depends  partly  upon  the  tariff  level  and  partly  upon  the  way  in  which  duties 
are  collected  (a  frontier  can  be  crossed  only  at  certain  designated  points) .  The  effect 
of  a  railway  line  that  cuts  through  a  town  is  similar. 


Some  New  Factors  201 

tioned  that  the  often  divergent  interests  of  individual  businesses 
within  a  state  determine  its  policy  and  size  to  a  rather  large  degree. 
The  safeguarding  of  profits  in  the  long  run  postulates  the  partici- 
pation of  business  leaders  in  politics,^^^  The  safeguarding  of  the 
power  of  the  state  in  the  long  run  demands  that  a  state  make  the 
economic  interests  of  the  citizens  its  own.  Exports  and,  when  neces- 
sary, imports  are  protected  if  possible  by  conquest,  by  command, 
or  by  treaties  in  regard  to  tariffs,  special  trade  privileges,  and  so  on. 
History  shows  how  closely  the  destiny  of  states  is  connected  with  that 
of  their  domestic  economy.  Italy  lost  her  commanding  economic 
position  in  the  Roman  Empire,  which  depended  upon  wine  and 
olive  oil  privileges,  and  her  political  pre-eminence  as  a  result,  when 
she  gradually  permitted  the  legions  to  supply  themselves  and  when 
she  gradually  emancipated  the  provinces  with  respect  to  these  and 
to  important  industrial  goods. ^^*  And  the  sway  of  the  Italian  com- 
mercial cities  came  to  an  end  when  the  old  trade  routes  to  the  Orient 
were  deserted  upon  the  discovery  of  a  sea  route  to  the  East  Indies. 
The  nature  of  the  British  economic  landscape  has  favored  the  crea- 
tion of  the  British  Empire  in  a  particularly  clear-cut  manner.  Size 
limitations  force  islands  to  make  the  most  of  their  limited  areas, 
while  at  the  same  time  their  position  offers  them  the  compelling 
advantage  of  far-flung  contacts."^  This  explains  the  difference  be- 
tween British  and  German  imperial  development.  As  ocean  freights 
are  so  low,  and  no  place  in  England  lies  much  more  than  about 
60  miles  from  the  sea,  she  is  as  closely  connected  with  other  maritime 
countries  throughout  the  entire  world  as  Germany  is  with  the 
adjoining  countries  of  Middle  Europe.  The  great  difference  between 
land  and  ocean  freights  sets  much  narrower  limits  for  the  Conti- 
nental emipres  than  for  those  oriented  toward  the  sea.^^^ 

The  simpler  and  more  uniform  are  economic  interests  within  a 
state,^"  the  clearer  and  more  productive  is  the  adjustment  of  politics 

153.  The  degree  of  participation  naturally  varies.  If  in  the  course  of  time  all  lose 
interest  (free  trade) ,  an  individual  entrepreneur  or  an  individual  people  have  less 
reason  to  enlist  political  power  in  the  service  of  economic  interests,  but  the  temptation 
to  do  so  increases. 

154.  See  M.  Rostovtzeff,  GeseUschaft  und  Wirtschaft  im  romischen  Kaiserreich 
(Leipzig,  1930)  ,  2  vols. 

155.  See  Ratzel,  op.  cit.,  pp.  356  ff. 

156.  Next  to  its  ideological  and  racial  homogeneity,  the  fact  that  its  economic  dis- 
tances are  much  shorter  than  its  geographic  is  undoubtedly  the  most  important  cause 
of  the  tenacious  cohesion  of  the  British  Empire.  (See  A.  Losch,  "  Die  Leistung  der 
Seeschiffahrt,"  Nauticus,  1941,  pp.  326-336.) 

157.  For  examples  see  A.  Predohl,  "  Staatsraum  und  Wirtschaftsraum,"  Weltwirt- 
schaftliches  Archiv,  XXXIX    (1934) ,  1/12,  p.  3. 


o,,^  Part   Two.     Ecoiioinic  Regions 

to  economics.  It  would  have  been  of  great  economic  advantage  to 
the  Confederate  States  of  America  if  they  had  succeeded  in  creating 
a  union  of  their  own.  Their  free-trade  policy  would  have  been 
approved  by  all  their  citizens,  and  would  therefore  have  been  able 
to  pursue  a  definite  course.  But  since  the  protectionist  industries 
of  the  North  and  the  free-trade  cotton  growers  of  the  South  live  in 
the  same  country,  American  policy  vacillates  between  moderate  and 
exorbitant  protective  tariffs  according  to  the  outcome  of  elections. 

§3.     Coincidence  of  Political  and  Economic 
Boundaries 

A  political  frontier  is  an  economic  boundary  also  when  by  nature 
it  is  hard  to  cross.  This  is  regularly  true  when  it  exists  for  significant 
reasons  such  as  natural  or  national  (racial)  barriers  especially.  Seas, 
lakes,  and  broad  rivers  keep  many  smaller  market  areas  from  further 
expansion,  exactly  as  do  mountain  chains,  deserts,  or  language 
barriers.^^^ 

Though  it  is  often  said  that  streams  connect  rather  than  separate 
their  banks,  this  is  so  only  for  trade  over  long  distances,  which  is 
cheaper,  though  not  quicker,  than  if  the  stream  were  solid  land. 
But  there  is  no  doubt  that  on  the  opposite  bank  the  sale  of  many 
goods  with  short  or  even  medium  shipping  distances  is  made  extra- 
ordinarily difficult,  and  the  more  so  the  wider  the  river  and  the 
fewer  therefore  its  bridges.  Since  states  aspired  to  natural  obstacles 
as  boundaries  until  the  awakening  of  national  consciousness  in  the 
nineteenth  century,  and  since  these  often  separate  peoples  as  well, 
many,  if  not  most,  of  today's  political  frontiers  are  also  natural 
boundaries  for  the  smaller  market  areas.  This  is  particularly  true 
for  retail  trade  and  artisans,  but  much  less  true  for  factories. 

The  coincidence  of  political  and  economic  boundaries  in  "  great 
spaces "  (Grossraiim)  is  desired  and  mutually  conditioned.  The 
leading  state  delimits  regions  of  influence  geographically  in  such  a 
way  as  to  include  wherever  possible  those  economic  conditions  that 
it  believes  important  for  its  existence,  and  to  this  extent  accommo- 

158.  This  refers  to  natural  boundaries.  Such  a  border  need  not  make  all  trade 
impossible,  nor  does  every  natural  obstacle  have  to  be  turned  into  a  political  frontier. 
Thus  a  natural  boundary  need  not  by  any  means  include  only  what  is  homogeneous. 
It  is  sufficient  that  the  state  enclosed  be  strong  enough  to  maintain  itself  by  reason  of 
its  size  and  economic  structure  and  the  suitability  of  its  border  for  military  purposes. 
In  my  opinion  Solch  asks  too  much  of  natural  boundaries  in  his  otherwise  admirable 
work  (J.  Solch,  Die  Auffassung  der  "  naturlichen  Grenzen  "  in  der  wissenschaftlichen 
Geographie  [Innsbruck,  1924])  . 


Some  New  Factors  203 

dates  itself  to  the  economy.  On  the  other  hand,  it  shifts  the  necessary 
foreign  trade  as  much  as  possible  to  easily  safeguarded  markets,  and 
here  the  economy  has  to  adjust  itself  to  the  policy  of  the  state.  Only 
when  that  which  is  important  for  existence  coincides  more  or  less 
with  that  which  can  be  defended  has  the  development  of  a  great 
space    {Grossraum)    succeeded. ^^^ 

§4.  Transformation  of  Economic  Areas 
BY  State  Boundaries'^" 

Larger  market  areas  are  always  transformed  along  political  fron- 
tiers, and  all  areas  are  changed  where  the  borders  represent  merely 
man-made  obstacles  to  trade.  We  can  classify  these  changes  into: 
first,  destruction  of  locations  or  their  removal  away  from  a  boundary, 
which  in  the  absence  of  disturbing  influences  together  create  the 
border  wasteland;  and  second,  removal  of  locations  across  the  border. 

a.  The  Border  Wasteland 
What  has  already  been  sketched  in  comparing  political  and  eco- 
nomic boundaries  may  now  be  supplemented. '^°''  Figure  53  shows 
at  the  left  a  few  typical  situations  at  the  border  of  economic  land- 
scapes; at  the  right,  at  the  border  of  two  countries.  The  relative 
position  of  the  regions  on  either  side  of  the  landscape  varies, 
depending  on  their  size  and  other  factors.  Since  they  are  oriented 
toward  different  centers,  they  do  not  necessarily  dovetail  with  each 
other.  The  political  boundary,  on  the  other  hand,  necessarily  cuts 
through  the  regular  networks  of  market  areas  unless  it  happens  to 
coincide  with  an  economic  boundary. 

159.  When  it  is  economically  profitable.  See  p.  339,  and  Losch,  Wesen  und 
Nutzen  zuirtschaftlicher  Grossriiume  (in  preparation  but  never  published)  .  The  pro- 
vision of  important  means  of  defense  obviously  will  never  be  wholly  guaranteed. 
Some  raw  material  obtainable  only  beyond  the  frontier  may  suddenly  acquire  signifi- 
cance, or  an  invention  may  be  made  there  that  may  be  more  threatening  than  any 
lack  of  raw  material,  which  often  can  be  made  synthetically  or  for  which  a  substitute 
can  frequently  be  found.  There  will  never  be  absolute  safety  in  any  region  smaller 
than  the  earth  itself.  It  must  also  be  considered  that  as  the  space  grows  in  size  more 
defensive  measures  are  needed  and  more  means  of  defense  provided,  for  larger  empires 
have  to  reckon  with  more  powerful  adversaries.  The  development  of  one  great  space 
starts  that  of  another.  All  depends  upon  which  increases  more  rapidly— the  need  for 
the  means  of  security,  or  their  supply. 

160.  For  transformation  within  states  especially  through  the  enormously  important 
transport  policies,  see  below,  pp.  345  ff. 

160a.  The  rest  of  this  paragraph  and  the  next  four  paragraphs  are  from  the  first 
German  edition  of  Die  rdumliche  Ordnung  der  Wirtschaft,  which  were  omitted  from 
the  second  edition  to  save  space.— Ed. 


204 


Part  Two.    Economic  Regions 


We  shall  discuss  first  the  individual  possibilities.  Area  1  remains 
unchanged,  because  the  economic  boundary  by  itself  has  no  effect 
whatsoever.  Area  12,  on  the  other  hand,  will  be  divided,  because 
the  political  border  reduces  the  demand  from  the  other  side  of  the 
border  and  because  the  total  demand  therefore  ceases  to  be  sufficient. 
The  size  of  the  neighboring  areas  will  thus  increase.  Areas  4,  5,  16, 
and  17  remain  unaffected.  Between  areas  2  and  3  parts  of  market 
areas  are  situated  whose  sources  of  supply  would  lie  on  the  other 


eti 


Fig.  53.    Economic  and  political  borders 

side  of  the  border  if  the  market  networks  could  expand  farther 
without  interference.  Depending  on  the  size  of  these  "  splinter  " 
areas  a  "  corner  "  area  will  arise,  which,  because  of  its  uneconomical 
shape,  will  extend  far  in  the  upward  and  downward  directions  in 
order  to  lead  to  a  sufficiently  large  sales  area,  provided  that  the 
other  areas  and  the  possible  sales  radius  permit  this  extension.  If 
the  splinters  are  small,  areas  2  and  3  will  expand.  The  same  is  true 
also  of  areas  6  and  7. 

It  is  different  with  areas  10  and  14,  whose  corners  are  also  cut 
off  by  the  boundary.  Area  10,  to  the  right  of  the  border,  and  area  14, 
to  its  left,  now  face  an  insufficient  demand.  They  will  therefore 
(at  least  at  first)  be  divided  among  the  neighboring  areas  which 
expand  correspondingly.  Areas  8  and  9,  which  overlap,  are  also  too 
small  when  taken  by  themselves.   But  they  can  be  consolidated  into 


Soi7ie  New  Factors  ^  •> 

a  fairly  large  new  market  area  whose  center  will  lie  on  the  boundary 
of  the  economic  landscape.  The  situation  is  similar  to  that  of  areas 
2  and  3  though  more  clear-cut.  So  much  for  the  temporary  solution 
of  the  typical  situations. 

These  derived  areal  extensions  do  not  last  in  all  cases,  however. 
By  changing  the  shapes  of  the  areas  and  by  a  movement  of  the 
locations,  additional  areas  may  be  created  here  and  there,  particu- 
larly along  the  economic  landscape  boundary,  and  most  probably  at 
corners  where  three  such  landscapes  meet,^"  because  splinters  of 
neighboring  landscapes  can  be  used  to  a  much  larger  extent  than 
would  be  the  case  where  three  countries  meet.^®^ 

Wherever  the  odd  pieces  are  not  sufficient  for  a  new  market  area, 
the  old  area  remains  enlarged.  The  sizes  of  the  areas  along  the 
border  and  within  it  are  equalized  only  if  the  surplus  is  sufficiently 
large  for  all  sales  areas  of  the  good  in  question  to  move  into  the 
next  higher  size  class,  but  too  small  to  permit  an  increase  in  the 
number  of  areas.  This  is  especially  probable  for  goods  with  a  large 
necessary  sales  radius. 

In  other  respects  state  and  economic  boundaries  have  the  same 
result:  The  market  areas  in  their  vicinity  are  larger,^*'^  and  therefore 
less  numerous."*  The  seam  at  the  boundary  gives  more  or  less  the 
impression  of  a  wasteland,  in  so  far  as  it  is  less  thickly  populated 
and  many  products  can  be  obtained  only  from  a  distance  or  not  at 
^}j  165  Prices  are  higher,  partly  because  more  freight  on  the  average 
is  added  to  the  factory  price  and  partly  because  there  is  less  com- 
petition. Boundaries  cause  economic  losses,  and  double  boundaries, 
economic  and  political,  mean  doubled  losses. 

161.  Such  triple  corners  are  surrounded  by  a  region  of  especially  numerous  over- 
lapping and  atrophied  market  areas.  But,  as  the  pieces  of  three  regions  may  be  con- 
solidated, more  enterprises  can  exist  here  than  at  any  other  point  along  the  border. 

162.  The  enterprise  locating  at  the  border  will  select  that  side  of  the  border  where 
the  empty  space  is  larger;  or,  if  it  is  not  much  smaller,  where  higher  tariffs  com- 
pensate for  the  smaller  size. 

163.  E.  H.  Chamberlin  shows  the  same  thing  for  a  boundary  beyond  which  there 
are  no  more  markets  (The  Theory  of  Monopolistic  Competition  [Cambridge,  Mass., 
1936  edition],  pp.  195-196.) 

164.  Adjustment  in  the  size  of  the  region  between  a  boundary  seam  and  the  interior 
of  an  economic  landscape  takes  place  only  when  the  surplus  is  large  enough  for  all 
sales  areas  of  the  product  concerned  to  rise  to  the  next  higher  order  of  size,  but  too 
small  to  permit  further  increase  in  the  number  of  areas;  that  is,  especially  in  the  case 
of  goods  with  a  large  necessary  shipping  distance. 

165.  This  is  true  also  of  economic  landscapes  where  the  necessary  sales  distance  is 
not  much  less  than  half  the  radius  of  the  landscape,  without  the  possible  sales  distance 
reaching  it. 


2o5  Ptirt  Two.     Economic  Regions 

All  these  consequences,  distortion  of  areas,  expansion  of  areas, 
and  dead  corners,  are  disproportionately  more  prominent  on  political 
frontiers.  Since  these,  unlike  economic  boundaries,  lower  the  demand 
from  remnants  of  areas  beyond  them,  and  since  they  often  entirely 
prevent  market  areas  from  extending  beyond  them,  industries  occu- 
pying gaps  are  still  less  common  and  market  areas  still  larger.  The 
number  of  unobtainable  products  is  greater,  too.  For  example,  the 
effects  of  tariffs  are  felt  most  in  the  boundary  seam  and  less  toward 
the  interior.  The  boundary  itself,  which  in  economic  landscapes  is 
the  location  of  many  enterprises  that  occupy  gaps,  is  most  deserted 
in  the  case  of  states;  for,  when  half  the  demand  comes  from  an 
adjoining  country  despite  the  political  frontier,"^  it  is  definitely 
more  advantageous  as  a  rule  to  move  production  there.  Exceptions 
referable  to  unusual  circumstances  will  be  discussed  in  the  statistical 
section. 

The  effect  of  political  frontiers  naturally  depends  entirely  on  the 
kind  and  size  of  the  barrier  that  they  set  up  against  trade;  but  under 
otherwise  similar  conditions,  products  with  small  necessary  shipping 
distances  are  hardest  hit.  First,  any  given  tariff  rate  has  a  more 
adverse  percentage  effect  when  low  freight  charges  are  added  to  the 
purchase  price  than  when  these  charges  are  high.  Second,  there  must 
be  added  to  the  customs  duties  all  the  annoying  formalities  at  the 
border,  which  cause  many  small  enterpreneurs  to  give  up  all  foreign 
trade.  A  third,  and  especially  important,  factor  is  the  technically 
necessary  limitation  of  the  number  of  border  crossings.  The  resulting 
increase  in  distance  between  a  seller  and  his  customers  is  relatively 
greatest  when  the  latter  are  near  the  border.^^^ 

13.    Shift  of  Location  to  an  Adjoining  State 

Suppose  that  country  B  is  large  enough  for  several  plants  of  a 
certain  sort,  but  that  in  country  A  there  is  a  place,  O,  with  con- 
ditions so  advantageous  for  production  that  the  entire  branch  of 
industry  is  concentrated  there  and  some  of  its  firms  supply  country 
B.    If  B  were  to  introduce  a  high  tariff  that  nullified  the  special 

166.  This  demand  originates  from  an  area  considerably  larger  than  half  the 
necessary  sales  area. 

167.  The  tariff  on  retail  goods,  which  typically  have  a  short  sales  distance,  is  calcu- 
lated from  the  high  retail  price;  that  on  wholesale  goods  from  the  much  lower  middle- 
man's price.  This  makes  no  difference  to  the  ultimate  consumer  if  the  retail  margin 
on  either  side  of  the  border  is  the  same  percentage  of  the  purchase  price  inclusive  of 
tariff. 


Some  Xru'  Factors  207 

advantages  of  O  in  so  far  as  sales  to  B  were  concerned,  the  firms  in 
question  would  migrate  from  A  to  B.^^^ 

Suppose,  again,  that  in  one  branch  of  industry  very  small  and 
very  large  enterprises  were  technically  possible,  and  that  one  or  the 
other  was  more  profitable  according  to  the  density  of  population. 
Suppose  that  a  few  of  the  large  enterprises  in  thickly  settled  country 
A  had  formerly  helped  to  supply  adjacent  parts  of  thinly  settled 
country  B  also.  But  suddenly  B  sets  up  a  high  tariff.  Suppose  that 
the  internal  demand  in  B  is  not  great  enough  for  very  large  enter- 
prises though  adequate  for  very  small  ones,  and  that  since  they  are 
no  longer  exposed  to  competition  from  large  enterprises  across  the 
border,  small  enterprises  spring  up  like  mushrooms.  Whereas,  in 
the  first  example,  a  long-established  enterprise  would  migrate,  in  the 
second,  only  a  newly  established  one  would  move  across  the  border. 
Canada  "^  provides  classic  examples  of  each,  as  does  also  the  shifting 
of  industries  after  the  partition  of  Austria-Hungary. 

A  country  poor  in  capital  may  be  well  adapted  to  the  working 
up  of  raw  materials  found  in  it,  but  foreign  capital  may  be  frightened 
away  by  uncertain  political  conditions  and  unpredictable  expro- 
priations. The  country  is  doubly  harmed:  it  loses  openings  for  its 
labor  because  foreign  entrepreneurs  finish  the  material  abroad,^^** 
and  it  is  further  exploited  through  high  risk  premiums. 

•y.    Economic  Width  of  a  Boundary 

Let  S  be  the  radius  of  a  rounded-off  state  and  L  the  radius  of 
an  economic  landscape.  The  lengths  of  the  two  are  decisive.  If  S 
is  shorter  than  L,  consumers  throughout  the  entire  state  may  under 
certain  circumstances  be  able  to  order  goods  with  relatively  large 
necessary  shipping  distance  (p  >  S)  from  abroad.  If  5  is  equal  to  L, 
then,  as  in  the  case  of  an  economic  landscape,  all  consumers  who  are 
more  than  S/2  away  from  the  capital  will  order  from  abroad.  If  S 
is  greater  than  L,  imports  may,  under  certain  circumstances,  be 
limited  to  a  narrow  border  seam.  Similarly  for  the  producer.  If  S 
is  shorter  than  L,  all  producers  may  be  able  to  export.    If  S  equals 

168.  See  Palander,  op.  cit.,  p.  331,  Fig.  83  and  text. 

169.  See  H.  Marshall  et  al.,  Canadian-American  Industry.  A  Study  in  International 
Investment   (New  Haven,  1936) . 

170.  For  example,  almost  all  Venezuelan  petroleum  is  refined  on  the  neighboring 
islands  of  Curacao  and  Aruba,  in  the  Netherlands  West  Indies.  Once  built,  such 
enormous  installations  can  be  moved  only  with  the  greatest  difficulty,  though  in  the 
meantime  Venezuela  has  developed  into  one  of  the  best-governed  countries  in  the 
world.   Of  course,  ocean  steamers  could  not  penetrate  to  the  oil  wells  in  any  case. 


2o8  P«''*  Two.     Ecnnomic  Regions 

L,  only  those  at  a  minimum  distance  of  2S/3  will  do  so.  If  S  is 
greater  than  L,  only  a  few  producers  in  a  very  narrow  border  seam 
may,  under  certain  circumstances,  export.^^^ 

From  this  reasoning  a  number  of  conclusions  may  be  drawn.  But 
first  it  is  well  to  remember  that  we  have  excluded  all  natural  differ- 
ences that  would  tend  to  increase  the  extent  of  foreign  trade.  For 
this  reason  our  conclusions  are  minimum  expectations,  since  some 
differences  will  always  exist  in  fact.  Second,  we  have  excluded  any 
state  intervention.  For  this  reason,  our  conclusions  would  be  the 
maximum  that  could  be  expected.  Since  the  effects  of  our  two 
assumptions  go  in  opposite  directions,  our  conclusions  show  a  sort 
of  average  picture  of  what  is  to  be  expected. 

(1)  The  width  of  a  boundary  is  the  same  for  all  economic  land- 
scapes, but  different  for  states.  (2)  The  effect  of  an  economic 
boundary  is  felt  halfway  to  the  center;  that  of  the  political  frontier 
of  a  large  state  only  in  the  boundary  seam,  and  of  a  small  state 
possibly  as  far  in  as  the  capital  itself.^'^  (3)  In  both  cases  the  eco- 
nomic influence  of  a  boundary  declines  toward  the  interior,  but 
is  greater  the  greater  are  the  necessary  sales  areas. ^''^^ 


§5.     Political   Economic   Areas 

These  are  economic  areas  that  exist  only  because  there  are  states, 
and  hence,  as  a  rule,  coincide  with  these  states.  Most  important  is 
the  area  over  which  an  economic  order  based  on  politics  extends. 
It  is  quite  conceivable  that  every  state  may  have  its  own  special 
principles  of  economic  organization.  In  the  face  of  such  funda- 
mentally different  political  beliefs  the  world-wide  acceptance  of 
capitalism  during  the  nineteenth  century  was  by  no  means  a  fore- 
gone conclusion. ^^* 

171.  When  state  frontiers  are  farther  a%vay  than  economic  landscape  boundaries, 
agricultural  products  also  are  artificially  diverted  from  their  natural  markets.  This  is 
hardest  for  the  farmers  concerned,  but  affects  those  economic  landscapes  as  well  that 
have  been  deprived  of  their  natural  boundary  zones.  Even  a  large  state  benefits  only 
to  a  limited  degree  from  this  diversion.  Because  of  increased  agricultural  supplies 
the  per  capita  income  of  the  inhabitants  of  its  central  economic  landscape  is  higher 
than  if  state  frontiers  and  economic  boundaries  coincided;  but  the  per  capita  income 
in  the  boundary  seam,  and  that  of  all  citizens  of  the  state  taken  together,  is  lower. 
The  costs  of  a  boundary  thus  appear  in  agriculture  exactly  as  in  industry. 

172.  Foreign  trade  is  therefore  more  important  for  small  countries  than  for  large. 

173.  Consequently  more  large  industries  than  small  are  interested  in  tariff  policies. 

174.  H.  von  Beckerath,  "  Politik  und  Wirtschaft,"  Schmollers  Jahrbuch,  LVI  (1932); 
"  Politische  und  Wirtschaftsverfassung,"  ibid.,  LVI    (1933) ,  258-276. 


Some  New  Factors  209 

The  second  profound  effect  that  may  originate  from  a  country 
is  the  creation  of  a  single  economic  landscape  embracing  its  entire 
area.  Just  as  it  is  advantageous  for  such  a  landscape  to  rise  to  state- 
hood, so  the  damage  is  at  least  reduced  when  a  state  develops  into 
an  economic  landscape.  This  assumes  three  things  above  all:  first, 
that  political  boundaries  represent  a  great  artificial  barrier  to  trade; 
second,  that  the  administrative  structure  of  a  state  is  of  great  eco- 
nomic importance;  third,  that  the  greatest  possible  extent  of  an 
economic  landscape  is  not  very  much  smaller  than  that  of  the  state. 

Furthermore,  individual  households  and  firms  in  the  same  state 
share  a  common  political  fortune.  We  have  learned  perfectly  what 
a  deep  influence  this  may  exert  upon  the  level,  the  source,  and  the 
stay  of  capital  imports. ^^^  It  is  wise,  also,  to  direct  the  export  of 
capital  in  accordance  with  political  alliances;  and  this  has  been 
widely  practiced  even  during  the  liberal  era,  if  only  because  invest- 
ment in  the  territory  of  a  possible  enemy  is  risky.^^^ 

But  even  market  areas  for  goods  proper  are  not  unaffected  by 
political  situations.  It  is  only  necessary  to  recall  the  political  boycott, 
or  it  converse,  a  preference  for  domestic  goods  for  patriotic  reasons. 
The  lessons  of  1871,  1918,  and  1933  show  how  greatly  national 
victory  or  defeat  can  exhilarate  or  depress  entrepreneurs  in  the  state 
concerned  and  lead  to  an  upswing  or  a  decline  in  the  national 
economy.  Wars  also  have  an  aftereffect  on  subsequent  business 
cycles.  They  raise  birth  waves,  and  when  these  have  been  trans- 
formed into  waves  of  marriages  and  in  the  labor  supply  they  cause 
cyclical  variations  in  the  economy.  At  least  it  was  so  in  Germany.^^^ 
Population  waves,  and  thus  business  cycles,  vary  characteristically 
in  amplitude  from  one  country  to  another,  since  the  immediate 
effects  of  wars  cease  abruptly  at  frontiers. ^^^ 

In  the  fourth  place,  a  state  may  represent  a  politically  created 
sales  area  for  goods  that  would  not  be  in  demand  at  all,  or  not  in 
this  state,  or  not  only  in  this  state,  or  not  everywhere  in  this  state, 

175.  Of  course  the  destiny  of  the  state,  with  which  the  national  economy  is  so  closely 
associated,  is  in  many  respects  nothing  but  a  higher  or  lower  import  duty  on  capital. 
It  determines  the  risk  premium  that  is  to  be  added  to  the  interest  rate. 

176.  A  form  of  risk  against  which  there  is  no  insurance. 

177.  A.  Losch,  "  Bevolkerungswellen  und  Wechsellagen,"  Beitrdge  zur  Erforschung 
der  wirstschaftlichen  Wechsellagen  Aufschwung,  Krise,  Stockung,  edited  by  A.  Spiethoff, 
Vol.  13   (Jena,  1936). 

178.  Similarly  the  domestically  conditioned  reluctance  of  American  industry  to 
make  investments  in  1937,  or  an  armament  boom  with  a  throttling  of  foreign  trade, 
had  effects  that  reached  at  first  almost  to  the  borders. 


210  Part  Two.     Economic  Regions 

without  pressure  from  above  such  as  tariffs,  taxes/^^  regulations,  or 
freight  rates.  It  must  be  clearly  understood,  however,  that  only  a 
few  customs  duties,  etc.,  have  such  effects.  In  the  case  of  public 
works  state  boundaries  are  generally  the  boundaries  of  the  possible 
supply  area  also. 

There  still  remain  to  be  mentioned  those  exceptional  cases  in 
which  economic  areas  created  by  a  state,  not  merely  controlled  by  it, 
do  not  coincide  with  the  state  itself.  Currency,  tariff,  and  political 
unions  need  not  coincide.  There  are  customs,  currency,  and  legis- 
lative frontiers  that  include  only  parts  of  states,  and  others  that 
embrace  several  states.  Consider,  on  the  one  hand,  customs  and 
mint  unions  or  the  identity  of  many  German  and  Austrian  laws 
after  World  War  I;  and  on  the  other  hand,  internal  customs  duties, 
significant  today  principally  in  trade  between  a  motherland  and 
her  colonies,  or  as  an  anachronism  still  to  be  seen  in  the  vicinity 
of  Paris,^^°  the  regional  validity  or  significance  of  many  laws,  and 
so  on.^^^ 

Finally,  in  many  respects  the  state  is  only  apparently  or  tem- 
porarily a  homogeneous  economic  area.  The  power  of  a  common 
monetary  system  to  create  regions  is  normally  but  slight,  as  will  be 
seen  in  Part  III.  The  opposite  experience  during  the  inflation 
period  and  since  the  last  crisis  was  exceptional.  Most  tariffs,  too, 
do  not  even  approach  the  creation  of  a  national  market,  or  even  a 
network  of  purely  domestic  market  areas.  As  a  rule  they  curtail 
only  the  tips  of  areas  that  extend  over  a  boundary.  Moreover,  there 
will  be  pointed  out  below  some  further  limitation  of  the  old  thesis 
that  production  factors  are  less  mobile  internationally.  If  it  was 
wrong  formerly  to  underestimate  the  importance  of  political  factors 
in  developing  economic  areas,  we  should  not  forget  today,  on  the 
other  hand,  that  this  is,  after  all,  but  one  influence  among  several. 


179.  The  method  of  computing  taxes  affects,  for  example,  the  construction  of 
automobiles. 

180.  These  were  reduced  in  1941  in  order  to  improve  the  food  supply. 

181.  W.  Sulzbach  gives  a  good  presentation  in  "  Der  wirtschaftliche  Begriff  des 
Auslands,"  Weltwirtschaftliches  Archiv,  XXXII  (1930)  .  For  the  many  trade  barriers 
between  individual  states  in  the  United  States  see  Works  Progress  Administration,  The 
Marketing  Laws  Survey,  Comparative  Charts  of  State  Statutes  Illustrating  Barriers  to 
Trade  Between  States    (Washington,  D.  C,  1939) . 


Chapter  14.     Further  Restriction  of  Market  Areas 


In  the  preceding  chapter  the  various  effects  of  individual  factors 
were  examined.  This  chapter  will  discuss  all  the  different  factors 
that  work  together  toward  the  same  end:  to  limit  the  extent  of 
narket  areas.  It  is  a  question  of  the  greatest  importance,  for  many 
will  doubt  whether  today's  low  freight  costs  are  of  sufficient  conse- 
quence to  restrict  markets  effectively. 

In  addition  to  freight  there  is  another  restraining  influence: 
competition.  But  where  freight  costs  are  of  little  importance,  com- 
petition by  itself  would  hardly  influence  the  limitation  of  market 
areas  and  the  distribution  of  production  sites.  Locations  would  not 
have  to  maintain  a  certain  distance  from  one  another,  and  all 
market  areas  would  overlap  everywhere.  Even  competition  can 
exert  its  limiting  effect  only  by  way  of  freight,  or  other  factors  that 
operate  similarly.  Here  it  is  immaterial  whether  these  factors  work 
by  raising  prices  to  the  consumer  or  by  lowering  the  profits  of  the 
producer.^  For  the  sake  of  simplicity  we  shall  limit  the  discussion 
to  the  former. 

(a)  Transport  costs.  The  freight  rate  sometimes  increases  with 
distance,  and  naturally  a  point  is  soon  reached  where  the  demand 
is  zero.  In  such  cases  the  argument  that  freight  costs  are  insignifi- 
cant falls  to  the  ground.  One  thinks  here  of  retail  stores,  laundries, 
breweries,  and  the  like  that  deliver  by  motor  truck  or  messenger  boy. 
With  increasing  distance  from  a  producer  the  density  of  habitations 
and  the  demand  of  individual  customers  drop,  partly  because  out- 
side of  large  cities  the  density  and  buying  power  of  the  population 
decrease  and  partly  because,  even  with  a  constant  freight  rate  and 
for  all  the  reasons  still  to  be  given,  both  this  particular  producer's 
proportionate  share  of  customers  and  the  inclination  of  individual 
customers  to  buy  become  smaller.  As  a  consequence  the  time  of 
the  motor  truck  or  of  the  messenger  boy  is  less  and  less  efficiently 
employed  with  increasing  distance,  and  there  remains  only  a  choice 

1.  In  the  latter  case,  revenue  cones  appear  in  place  of  price  funnels.  Curves  for 
equal  gross  receipts  were  probably  first  used  by  V.  Furlan,  "  Die  Standortprobleme  in 
der  Volks-  und  Weltwirtschaftslehre,"  Weltwirtschaftliches  Archiv,  II    (1913). 


212  Part  Two.    Economic  Regions 

between  charging  distant  customers  for  delivery  or  abandoning 
delivery  beyond  a  certain  point.  Costs  resembling  freight  have  the 
effect  of  higher  freight  rates.  Among  these  are,  in  particular,  insur- 
ance and  the  deterioration  of  goods  in  transit— not  during  loading 
and  unloading,  since  these  are  fixed  costs. 

(b)  Time  costs.  These  are  disadvantages  that  arise  not  so  much 
from  the  overcoming  of  distance  as  from  the  time  that  this  requires. 
In  this  category  belongs  the  time  lost  by  the  housewife  in  making 
her  purchases,  no  less  than  the  time  that  elapses  between  the  ordering 
of  goods  and  their  delivery.  The  monetary  cost  of  time  appears  in 
various  guises:  as  interest  on  the  sum  invested  in  goods  in  transit; 
as  an  additional  charge  for  quick  delivery;  as  the  cost  of  larger 
inventories  to  the  retailer,  for  whom  a  distant  factory  is  not  a  reserve 
warehouse  in  the  same  measure  as  one  that  is  near  by;  or  as  loss  of 
business  if  goods  cannot  be  delivered  in  good  time.^ 

(c)  Selling  costs.  The  cost  of  sales  promotion  increases  with 
distance.  The  time  of  a  commercial  traveler  cannot  be  so  profit- 
ably employed,  for  example,  when  buyers  are  thinly  distributed,  and 
similarly  a  newspaper  advertisement  draws  a  smaller  response. 
Furthermore,  one  must  understand  one's  market,  and  keep  well 
informed  on  current  trends.  This  often  happens  automatically  when 
a  market  is  near,  but  involves  costs  in  the  case  of  more  distant  ones. 
Branches  and  representatives  cause  additional  expenditures,  and  the 
outlay  for  postage,  telephone,  and  travel  is  also  greater. 

(d)  Business  risks.  Risks  generally  increase  with  distance.  Far 
too  little  attention  is  paid  to  this  fact,  but  it  will  receive  concrete 
proof  in  the  statistical  section.  Long  distances  make  it  difficult  to 
get  reliable  information  on  the  credit  and  needs  of  buyers,  as  well 
as  on  the  legal  methods  to  be  taken  in  respect  to  payment  should 
these  become  necessary.^  This  fact  in  its  turn  is  used  to  their  advan- 
tage by  a  less  desirable  class  of  buyers. 

(e)  Idiosyncrasies.  Most  products  are  adapted  to  the  character- 
istics of  their  own  limited  markets— to  climate,  habits,  income,  and 
so  on.  Thus  the  demands  of  a  more  distant  neighborhood  are  not 
so  easily  met. 

2.  Quick  delivery  plays  a  role  especially  in  the  case  of  fashionable  articles.  It  may 
even  determine  location,  as  E.  M.  Hoover  has  shown  in  his  admirable  study  of  the 
shoe  industry.  Location  Theory  and  the  Shoe  and  Leather  Industries  (Cambridge, 
Mass.,  1937) ,  p,  176. 

3.  According  to  German  law,  payment  has  to  be  made  at  the  domicile  of  the  buyer 
unless  another  place  has  been  stipulated  in  the  contract. 


Further  Restriction  of  Market  Areas  213 

(f)  Extent  of  business.  Even  though  the  spatial  expansion  of 
a  business  entails  no  particular  costs,  nevertheless  such  costs  arise 
after  a  certain  point,  when  the  physical  p]:;nt  of  the  business  has 
to  be  enlarged  as  a  consequence.  This  factor  does  not  become 
operative  immediately  with  plants  that  work  to  the  left  of  the  point 
of  minimum  average  costs,  iDut  with  continued  expansion  it  makes 
itself  felt  eventually. 

(g)  Hindrances  to  trade.  Sooner  or  later  the  sale  of  most  goods 
encounters  governmental  barriers.  In  the  Middle  Ages  especially 
there  were  countless  road  taxes,  excise  taxes,  and  customs  duties  to 
be  surmounted,  and  since  the  1870's  the  weight  of  such  restrictions 
has  been  increasing  again. 

(h)  Disinclination  and  incompetence.  The  difficulties  of  the 
entrepreneur  increase  with  the  growth  of  his  sales,  and  particularly 
with  the  distance  of  his  customers.  How  many,  for  example,  give 
up  foreign  trade  because  of  the  formalities  associated  with  it!  More- 
over, a  lack  of  ideas  and  imagination  in  most  entrepreneurs  precludes 
more  distant  connections. 

Thus,  over  and  above  its  immediate  costs,  distance  plays  a  role 
in  everything  that  is  individual  and  that  presupposes  thorough 
knowledge  and  confidence— a  role  that  men  often  neglect  to  their 
cost.  Even  when  more  distant  buyers  are  no  longer  served  directly, 
but  through  distributors  or  branches,  these  can  only  mitigate  the 
effect  of  distance,  not  remove  it.  This  effect  is  evident,  indeed,  far 
beyond  the  sphere  of  economics.  It  is  more  difficult  to  hold  large  or 
misshapen  empires  together,  and  as  a  rule  it  can  be  done  only  at  the 
expense  of  native  individuality.  Even  the  proportion  of  Catholics 
in  Europe  decreases,  by  and  large,  with  their  distance  from  Rome.^-^ 

There  is  a  strong  inclination  to  disregard  the  laws  of  distance, 
and  for  a  long  time  this  tendency  was  esteemed  as  progress.  Trade 
was  no  longer  regarded  as  determined  by  such  immediately  experi- 
enced realities  as  local  and  regional  relationships,  but  by  abstract 
ideas,  universal  principles,  guiding  maxims,  or  general  laws,  that 

4.  Not  their  proportion  in  a  single  place,  but  their  proportion  among  the  people 
of  each  individual  but  not  too  narrow  ring.  Similarly,  Mecca  and  Medina  lie  at  the 
geographical  center  of  the  Mohammedan  world. 

5.  In  the  field  of  sociology  compare:  the  sphere  of  marriage,  migrating  supply  areas 
(examples  in  Bevolkerungshiologie  der  Grosstadt,  edited  by  E.  von  Eikstedt  [Stuttgart, 
1941],  p.  242)  ,  and  the  distribution  of  students.  The  percentage  of  persons  subject  to 
punishment  often  decreases  with  distance  from  the  center  of  a  city,  and  so  on.  (See 
R.  D.  McKenzie,  The  Metropolitan  Community  [1933],  p.  185. 


Part   Tivo.     Economic  Regions 
214 

met  the  needs  of  any  one  place  only  very  roughly.  They  did  away 
with  a  great  deal  of  narrow-minded  whimsey,  but  at  the  same  time 
with  much  that  had  grown  to  be  of  solid  value.  It  will  be  shown 
in  the  statistical  section  that  this  contempt  for  distance  caused  great 
losses,  economic  and  otherwise,  for  the  saying  of  Saint  Thomas 
Aquinas  on  indinatio  rerum  in  proprios  fines  "  still  holds  true. 


6.  The  tendency  of  things  to  stay  within  tlieir  own  limits. 


Chapter  15.     Economic  Regions  in  Reality  ^ 


a.     SPATIAL    ARRANGEMENT 

The  two  preceding  chapters  considered  separately  the  various 
causes  or  the  various  effects  of  the  same  phenomenon.  It  is  now 
necessary  to  combine  the  resuks  of  both  methods  of  study  and  draw 
a  complete  picture. 

§1.     Market   Areas 

When  we  drop  the  assumption  of  a  uniform  plain,  the  simple 
market  and  supply  areas  assume  irregular  shapes  and  sizes  because 
of  the  natural,  personal,  and  political  differences  already  mentioned. 
Furthermore,  market  areas  for  the  same  product  overlap,  since  it  is 
seldom  finished  in  exactly  the  same  way,  and  each  area  is  fringed 
out  in  consequence.  Nevertheless,  our  original  simplifying  assump- 
tions often  seem  to  be  more  or  less  fulfilled,  and  in  such  cases  our 
theoretical  findings  will  hold  without  much  change.  A  few  examples 
will  be  offered  in  the  statistical  section, 

§2.     Regional   Networks 

Since  market  areas  for  the  same  product  overlap,  as  has  just 
been  said,  strictly  speaking  they  can  no  longer  be  compared  with  a 
network.  They  are  more  like  an  irregular  layer  of  pieces  of  slate, 
carelessly  flung  down.  The  essential  properties  of  a  network  are 
usually  retained,  however,  and  hardly  a  single  chart  of  market  areas 
represents  them  otherwise.  But  there  is  another  modification  of  the 
network  that  is  of  great  importance.  We  assume  that  networks  would 
cover  the  whole  plain,  though  in  reality  their  extent  is  more  or  less 
restricted  and  we  speak  then  of  districts  and  belts,  according  to 
whether  only  production  sites  or  their  market  areas  as  well  are 
circumscribed  as  to  space.  Such  a  concentration  may  be  based  on 
external  economies  or  depend  upon  the  limited  scope  of  natural 
or  political  factors.   This  is  especially  clear  when  these  factors  them- 

1.  Based  in   part   on   my   lecture,   "The   Nature  of   Economic   Regions,"  Southern 
Economic  Journal,  V    (1938)  ,  71. 


2i6  Pai^t  Two.    Economic  Regions 

selves  create  certain  market  networks.  Yet  it  is  not  necessarily  true 
that  these  extra-economic  factors  and  their  economic  result  coincide. 
Cotton  is  not  grown  wherever  it  will  thrive,  nor  is  it  always  spun 
where  it  is  cultivated.^ 

§3.     Regional   Systems 

Economic  landscapes,  the  highest  and  most  complicated  form  of 
economic  area,  differ  most  of  all  from  the  simplified  theoretical 
picture.  It  is  simply  impossible  to  arrange  all  the  irregular  and 
often  spatially  bound  networks  in  such  a  way  that  they  will  have 
at  least  one  common  center.  Actually  there  is  no  longer  an  eco- 
nomically self-sufficient  economic  landscape,  nor  is  there  a  metropolis 
in  which  all  industries  are  fully  represented.  And  this  is  not  all. 
In  fact,  one  might  imagine,  and  perhaps  even  discover,  a  few  cases 
where  economic  landscapes  exchanged  their  specialties  exclusively 
by  way  of  their  capitals.^  Under  these  circumstances  every  economic 
landscape  would  still  be  as  compactly  organized  as  in  our  ideal 
system.  However,  it  would  be  better  then  to  speak  of  economic 
districts,  or  economic  provinces,  because  these  words  express  more 
clearly  the  fact  that  we  are  no  longer  dealing  with  independent, 
economically  self-sufficient  units.  In  reality,  not  only  do  entire  dis- 
tricts depend  on  other  capitals  for  certain  specialties;  ^  for  many 
goods,  small  places  that  otherwise  depend  completely  upon  neigh- 
boring larger  towns  are  centers  of  extensive  market  areas  that  reach 
far  beyond  the  home  district,  and  may  even  include  the  whole  world. 
Again,  whereas  every  regional  system  has  a  large  town  for  its  center, 
every  large  town  is  not  the  center  of  such  a  system.  Many  large 
mining  towns,  for  example,  can  hardly  be  said  to  fulfill  an  economic 
function  for  their  environs.^   From  such  specialized  large  towns  the 

2.  Spinning  mills  in  the  United  States  are  concentrated  in  the  eastern  part  of  the 
cotton  belt. 

3.  One  of  the  two  most  important  functions  of  the  central  town  is  then  to  establish 
connections  with  the  remaining  economic  landscapes.  The  other  is  trade  with  its  own 
economic  landscape. 

4.  O.  Schiller  ("Die  Landschaften  Deutschlands,"  Allgemeines  Statistisches  Archiv, 
XX  [1930],  24-41)  even  goes  so  far  as  to  maintain  that  in  Germany  only  the  following 
cities  are  morfe  or  less  autocrats  in  their  economic  landscapes:  Berlin,  Stettin,  Konigs- 
berg,  Breslau,  Munich,  Vienna,  and  Stuttgart. 

5.  Hence  they  often  show  extraordinary  fluctuations  in  population.  The  gold-mining 
town  of  Cripple  Creek,  in  Colorado,  for  instance,  had  45,000  inhabitants  in  its  heyday, 
and  only  4,000  in  1930.  But  after  the  depreciation  of  the  dollar  the  old  mines  became 
profitable  once  more,  and  the  population  rose  quickly  to  7,000.  (C.  Goodrich  et  al., 
Migration  and  Economic  Opportunity  [Philadelphia,  1936],  p.  271.) 


Economic  Regions  in  Reality  217 

major  cities  of  districts  are  distinguished  by  the  diversification  of 
their  production,  or  at  least  of  their  trade,  which  provides  abundant 
connection  with  their  environs. 

Amid  all  the  chaos  of  reality  a  basic  pattern  of  economic  districts 
is  nevertheless  unmistakable.  These  differ  from  the  ideal  economic 
landscape  in  one  important  point:  they  are  not  self-sufficient.  They 
coincide  with  it  in  so  far  as  they  are  established  on  the  same  prin- 
ciples—the advantages  of  a  large  local  demand  and  traffic  density. 

These  principles  suffice  to  call  economic  landscapes  into  being, 
as  we  have  already  seen  in  the  theoretical  derivation.  But,  second, 
the  hierachy  of  markets  may  depend  also  upon  the  hierarchy  of 
administrative  areas.  Third,  it  may  originate  in  natural  or  national 
factors  of  an  areal  nature  as  does  a  region  of  agricultural  mono- 
culture (cultivation  of  a  homogeneous  product)  or  a  racial  manner 
of  life  (homogeneous  consumption)  .^  Thus  cotton  growing  deter- 
mined for  a  long  time  the  spatial  organization  of  the  economy  in 
the  American  southern  states.  The  supply  regions  of  15,000  cotton 
gins,  which  cleaned  the  cotton  and  removed  the  seeds,  were  super- 
imposed upon  the  producing  areas  of  the  individual  plantations; 
above  these  came  the  wider-meshed  network  of  presses;  "^  above  these, 
again,  the  500  oil  mills;  then  the  transport  points;  the  collecting 
depots,  where  the  cotton  is  sorted  and  stored;  and,  at  the  top,  the 
two  principal  export  ports  with  their  enormous  supply  regions.^  The 
arrangement  of  the  networks  of  the  distributing  trades  was  largely 
patterned  after  those  of  the  all-controlling  cotton  production.  {Ibid., 
p.  190.) 

6.  In  the  last  case  the  networks  of  market  areas  for  a  whole  series  of  goods  are  of 
similar  extent;  not  accidentally,  but  because  these  goods  represent  a  meaningful  com- 
bination. This  is  enough  to  delimit  an  entire  group  of  economic  landscapes,  if  not 
from  one  another  then  at  least  from  without. 

7.  As  a  heavy  press  costs  about  $50,000,  it  would  not  pay  the  individual  cotton  gin, 
with  an  average  yearly  output  of  only  1,000  bales,  to  buy  one.  A  profitable  press  will 
take  care  of  the  output  of  some  30  gins  and  has  a  supply  region  of  perhaps  50  miles' 
radius,  as  compared  with  less  than  10  miles  for  gins.  These  provide  an  interesting 
example  of  the  stickiness  of  a  once  firmly  established  location  pattern.  Formerly  the 
supply  region  for  cotton  gins  had  a  radius  of  roughly  5  miles,  but  with  their  improve- 
ment and  with  better  roads  the  most  advantageous  size  of  the  supply  area  increased. 
But  this  more  advantageous  size  of  the  supply  area  is  realized  only  in  the  new  cotton 
area  west  of  the  Mississippi  River,  where  individual  gins  work  up  on  the  average  one 
third  more  cotton  than  those  in  the  old  cotton  area.  (E.  S.  Moulton,  "  Cotton  Produc- 
tion and  Distribution  in  the  Gulf  Southwest,"  U.  S.  Department  of  Commerce,  Domestic 
Commerce  Series  No.  49  [Washington,  D.  C,  1931],  p.  46)  . 

8.  Only  the  cotton  of  the  Southeast  is  spun  near  by,  as  a  rule,  which  gives  rise  to 
many  small  supply  regions. 


2i8  P^''^!'  Two.     Economic  Regions 

Regional  substrata  like  this  are  to  be  found  almost  everywhere, 
but  they  are  not  always  of  equal  importance.  Their  importance  is 
inversely  proportional  to  that  of  market  areas  that  do  not  fit  into 
the  economic  landscape  pattern.  In  south  Germany,  for  example, 
these  substrata  are  of  the  highest  importance,  as  Christaller  has  so 
convincingly  shown.^-^"  In  the  Ruhr,  on  the  contrary,  it  is  difficult 
to  find  any  at  all."  According  to  the  regularity  of  spatial  organiza- 
tion, a  regional  substratum  will  be  regarded  as  the  essence  in  one 
case,  whereas  in  another  it  may  be  thought  irrelevant  and  left 
entirely  out  of  consideration.  However  suitable  a  regional  point  of 
view  may  be  for  many  areas,  it  would  be  difficult  and  profitless  to 
attempt  the  complete  subdivision  of  a  large  country  into  economic 
landscapes.^^ 

Finally,  economic  and  political  or  cultural  landscapes  share 
essential  features  in  their  structures.  All  have  a  central  point,  for 
example.  In  fortunate  cases  their  central  points  coincide,  and  then 
there  arises  one  of  the  world's  great  centers  of  power. 

§4.      S  U  M  M  A  R  Y 

We  have  found  three  main  types  of  economic  regions:  simple 
market  areas,  regional  networks,  and  regional  systems.  Or  to  impress 
the  matter  more  clearly  we  may  speak  of  markets,  belts,  and  districts. 

9.  W.  Christaller,  Die  zentralen  Orte  in  Suddeutschland    (Jena,  1933),  pp.  165-251. 

10.  The  economic  capitals  Frankfort,  Nuremberg,  Munich,  Zurich,  Strasbourg,  and, 
at  the  center,  Stuttgart,  are  very  evenly  distributed. 

11.  Unless,  like  Schlier  (op.  cit.,  p.  37),  one  combines  the  regions  of  influence  of 
the  rival  Rhenish-Westphalian  centers,  thus  obtaining  a  larger  economic  lanscape  that 
is  split  through  the  center.  On  the  other  hand,  see  Isenberg,  "  Zur  Stadtplanung  in 
den  neuen  deutschen  Ostgebieten,"  Raumforschung  und  Raumordnung,  1941,  pp.  141  f. 

How  clearly  the  supply  regions  for  individual  partial  centers  can  be  separated  is 
seen  in  the  simple  example  of  the  twin  cities  St.  Paul  and  Minneapolis.  Even  when 
their  economic  functions  in  general  are  at  all  similar,  the  regions  they  control  are 
clearly  distinguished.  The  hinterland  of  Minneapolis  stretches  toward  the  west,  whereas 
the  more  easterly  St.  Paul  commands  the  east.  (See  M.  L.  Hartsough,  The  Twin  Cities 
as  a  Metropolitan  Market  [Minneapolis,  1925],  p.  13.  The  case  of  Leeds  and  Bradford 
is  similar.    (Stamp  and  Beaver,  The  British  Isles  [London,  1937],  p.  573.) 

12.  Yet,  according  to  K.  Haushofer  ("  Grosstadtprobleme  der  Monsunlander," 
Archiv  fiir  Bevolk.,  1942,  p.  268) ,  Japan  is  made  up  entirely  of  cells  having  about  the 
same  shape,  and  the  size  of  a  district;  small  river  drainage  basins  with  urban  centers 
"  that  fit  together  like  the  cells  of  a  honeycomb."  And  Isenberg  (op.  cit.,  p.  266) 
found  an  astonishingly  regular  substratum  for  the  most  dissimilar  parts  of  Germany. 
Even  a  good  many  disturbances  may  not  greatly  change  the  regularity  of  the  structure. 
(J.  Umlauf,  "  Der  Stand  der  Raumordnungsplanung  fiir  die  eingegliederten  Ostgebiete," 
Neiies  Bauerntum,  1942,  p.  287,  map  of  the  Regierungsbezirk  Posen.) 


Economic  Regions  in  Reality  219 

The  members  of  this  series  become,  in  that  order,  increasingly 
complicated,  increasingly  self-sufficient,  but,  unfortunately,  increas- 
ingly uncommon  too. 

On  the  one  hand  we  have  simple  supply  or  market  areas— very 
simple  indeed,  manifestly  real,  and  wholly  dependent  upon  trade. 
The  systems  of  market  areas  or  districts  are  the  antithesis.  Their 
structure  is  anything  but  simple.  In  the  ideal  case  of  a  "  landscape  " 
they  are  wholly  self-sufficient,  but  seldom  can  they  be  found  so 
distinct.  Many  goods  remain  outside  every  such  system.  And  what- 
ever systems  we  find  overlap  still  more  than  simple  markets.  A 
clearly  defined  economic  landscape  is  a  piece  of  good  fortune 
rather  than  a  natural  subdivision  of  a  state.  Nevertheless  a  sub- 
stratum resembling  an  economic  landscape  is  to  be  found  almost 
everywhere  below  a  maze  of  market  areas,  though  developed  to 
different  degrees. 

Between  the  simple  market  area  and  the  complete  economic 
landscape  comes  the  network— that  is,  the  totality  of  all  market  areas 
for  the  same  product.  The  network  itself,  or  at  least  its  heart,  is 
often  compressed  into  a  narrow  space.  Such  belts,  or  zones,  of  homo- 
geneous production  or  consumption  arrest  our  attention,  but  they 
should  not  be  confused  with  economic  landscapes.  The  economic 
landscape  is  a  system  of  different  markets;  an  organism,  not  merely 
an  organ. 

b.     ON    A    CHAOTIC    INTERPRETATION 

No  doubt  the  spatial  economic  pattern  about  us  contains  enough 
illogical,  irregular,  lawless  features.  But  I  refuse  to  put  the  whole 
emphasis  on  this  lack  of  order.  No  matter  how  widely  a  chaotic 
interpretation  may  be  confirmed  by  the  facts,  it  is  not  only  unworthy 
but  dangerous.  Unworthy  because  there  is  also  a  reality  of  reason, 
upon  which  incomparably  more  depends  in  the  long  run  than  upon 
the  reality  of  the  factual.  Dangerous  because  our  idea  of  reality  is  one 
of  the  factors  that  shape  the  future.  Had  only  obstacles  to  the  opera- 
tion of  logical  and  natural  forces  been  emphasized  and  fostered  at 
the  dawn  of  capitalism,  this  would  never  have  been  able  to  complete 
its  great  achievements.  It  needed  no  planning;  indeed,  could  despise 
planning  as  a  "  disturbance,"  since  it  believed  in  the  great  principles 
of  its  time  and  lived  in  accordance  with  them.  It  rose  with  belief 
and  declined  with  unbelief  in  its  own  order.  In  the  face  of  a  belief 
in  an  orderly  progress  or,  more  accurately  stated,  in  its  possible 
functioning,  chaotic  facts  automatically  lose  their  significance.  This 
belief  is  based  on  nature  and  reason  when  it  can  no  longer  depend 
on  the  facts.  From  them  it  creates  the  model  for  an  order  that  may 
originate  only  as  a  result  of  it. 


220  Part  Two.    Economic  Regions 

The  roots  of  anarchy?  There  is  a  chaos  that  arises  from  doubt 
and  despair,  a  parasite  upon  order  when  it  reminds  us  of  the  tem 
poral  nature  of  all  human  ordering,  even  though  occasionally  it 
may  fructify  order.  But  there  is  another  sort  of  chaos,  which  is 
really  nothing  but  order  in  disguise.  Thus  the  bewildering  indivi- 
duality of  various  places  and  events  in  space  may  arise  merely 
because  each  consists  of  a  special  combination  of  different  orders- 
geographical,  geological,  political,  racial,  religious,  and  so  on— which 
interfere  with  one  another  and  cause  tensions  but  do  not  destroy 
each  other's  roots.  The  economic  sphere  is  simply  added  to  the 
many  other  spheres  of  life  that  overlap,  neither  dominating  nor 
merely  tolerated. 


PART   THREE.      TRADE 


A.   Description  of  Equilibrium 


Chapter  16.     Six  Cardinal  Problems  of  the  Division  of  Labor 
and  Their  Interrelations  ^ 


OUR  THEME  is  the  combination  of  man,  work,  and  place. 
Seen  from  the  standpoint  of  man  it  is  the  problem  of  the 
occupational  and  spatial  division  of  labor.  Often  enough,  however, 
we  do  not  start  with  ourselves,  but  wish  to  know  what  combination 
will  be  best  for  an  enterprise  or  a  country.  For  this  reason,  only  the 
following  six  questions  together  will  cover  the  subject  completely 
(see  Fig.  54)  . 

These  are  already  more  or  less  familiar  to  us  in  another  form: 

1.  The  problem  of  choice  of  an  occupation. 

2.  The  problem  of  the  cooperation  of  men  in  an  enterprise. 

3.  The  problem  of  selecting  a  place  to  live    (the  emigration 
problem)   and  of  the  distribution  of  populations. 

4.  The  problems  of  urban  sociology. 

5.  The  "  chamber  of  commerce  "  problem  (the  developmental 
possibilities  of  a  town) . 

G.    The  traditional  location  problem. 

We  thus  place  in  a  broader  context  the  sixth  problem,  the  main 
one  considered  hitherto. 

1.  Here  we  discuss  only  the  nature,  not  the  cause,  of  the  division  of  labor.  In  the 
final  analysis  the  cause  would  be  our  old  familiar  trio:  site,  supply,  and  volume;  that  is, 
natural  differences  in  and  advantages  of  mass  production  or,  as  Ohlin  and  Iversen 
express  it,  a  lack  of  mobility  and  divisibility.  A  historical  treatment  would  have  to  take 
developmental  stages  into  account  as  well.  E.  W.  Zimmermann  {Foreign  Trade  and 
Shipping  [New  York,  1918],  pp.  40  f.)  has  hit  upon  the  distinction,  very  pretty  in  itself, 
that  because  of  developmental  differences  world  trade  today  still  definitely  follows 
latitude,  whereas  in  the  future,  when  only  climatic  differences  remain,  it  will  have  to 
follow  longitude— a  concept  upon  which  is  based  the  idea  of  establishing  world  eco- 
nomic areas.  It  forgets,  however,  that  site  and  volume  also  lead  to  trade.  Furthermore, 
the  concept  of  supply  must  be  broad  enough  to  include  human  capabilities  also. 

223 


224 


Part  Three.     Trade 


The  preliminary  answer   to  all  six  questions  may   seem   very 
general  at  first,  or  even  naive.    It  amounts  in  each  case  to  a  maxi- 
mization  (of  production,  of  utility,  of  financial  return,  and  so  on) 
that  is  felt  to  be  self-evident.    We  endeavor  to  make  the  most  of 
every  situation.    But  it  will  soon  be  realized  that  all  more  exact 


Fig.  54.    Schematic  representation  of  the  six  basic  questions  of  the  division  of  labor 

and  detailed  solutions,  which  interest  us  much  more,  can  be  derived 
from  this  general  solution  only  by  abandoning  full  understanding 
of  the  situation.  The  mathematical  determination  of  the  optimum 
transport  point,  for  example,  is  infinitely  more  impressive  as  a  solu- 
tion of  the  location  problem  but  also  incomparably  less  accurate 
than  the  statement  that  an  entrepreneur,  all  things  considered,  will 
establish  his  enterprise  at  a  place  that  he  likes  best.  We  shall  do 
well  to  recall  from  time  to  time  the  limited  validity  of  our  precise 
formulas,  in  order  not  to  overlook  the  fact  that  they  merely  help  us 
in  arriving  at  a  decision;  in  themselves  they  do  not  provide  one. 

Even  the  most  carefully  considered  conclusion  is  only  an  experi- 
ment after  all.  It  is  like  shooting  when  we  are  neither  certain  of 
the  target  nor  able  to  test  how  close  we  have  come  to  it.  In  the 
last  analysis,  of  course,  we  say  that  we  have  been  aiming  at  the 
highest  utility,  and  many  believe  themselves  able  to  measure  it. 
But  to  balk  at  words  would  be  petty.  Utility  may  signify  the  general 
good  as  well  as  personal  happiness,  and  efforts  may  be  directed 
toward  it  either  from  a  sense  of  duty  or  by  inclination. ^  And  yet— 
we  have  agreed  upon  a  vague  word  that  any  critic  will  be  able  to 
pick  to  pieces!    The  real  difficulty  in  all  measurements  of  utility 

2.  But  in  every  case  only  such  efforts  as  accord  with  the  economic  principle  in  the 
sense  developed  on  p.  184,  note  118. 


,S/x  InLerrelaled  Problems  225 

lies  in  the  fact  that  we  have  no  idea  of  what  "  utility  "  actually  is. 
Often  we  surmise  its  meaning,  to  be  sure,  but  frequently  enough 
we  decide  upon  one  of  two  mutually  exclusive  courses,  not  because 
it  seems  preferable,  or  because  it  makes  no  difference  to  us,  but 
because  something  or  other  must  finally  be  done.  Every  choice 
naturally  gives  the  impression  that  the  greater  utility  has  been 
selected.  But  why,  then,  is  there  so  often  pain  at  having  to  forego 
one  possibility  after  another  preferable  one  has  been  chosen?  We 
should  not  feel  this  distress  if  the  case  were  merely  one  of  deciding 
between  two  and  four  units  of  utility,  as  between  two  coins.  Here 
we  meet  an  obstacle  so  fundamental  that  we  cannot  circumvent  it 
by  the  little  trick  of  "  indifference  curves."  In  reality  these  curves 
do  not  avoid  the  concept  of  utility,  but  merely  conceal  it.  The  shape 
of  utility  curves  can  be  reconstructed  from  them.  Indeed,  they  pre- 
suppose a  better  knowledge  of  utility  than  do  the  ordinary  decisions 
of  mankind.  For  one  may  prefer  one  object  to  another  that  costs 
the  same  without  being  able  to  say  how  much  more  utile  it  seems, 
but  the  value  of  a  combination  of  foods  cannot  be  equated  with 
that  of  another  combination  without  a  very  exact  idea  of  their  utility. 
Choice  becomes  especially  difficult  in  the  neighborhood  of  the  equi- 
librium of  marginal  utilities. 

We  must  not  deceive  ourselves  (and  we  do  v/ell  to  remember 
this  when  we  are  in  danger  of  being  too  sure  of  our  results)  by  the 
thought  that  with  the  introduction  of  the  concept  of  utility  we  have 
firmly  founded  our  science  in  the  unknowable;  and  yet  no  other 
course  remains  if  we  wish  to  pursue  it.  Though  we  know  that  in 
the  end  we  always  must  act  with  our  fingers  crossed,  through  a 
curious  yet  wholly  reasonable  quirk  in  our  nature  we  seek  for  the 
meaning  of  the  single  act,  and  for  the  higher  order  into  which  all 
events  fit.^  We  act  as  though  we  understood  the  purpose  of  life,  and 
hence  could  classify  routes  according  to  the  speed  with  which  they 
lead  to  its  goal.  We  interpret  economic  activities  as  if  they  aimed 
at  the  highest  utility,  reading  into  them  a  rational  design  that  may 
be  lacking  in  reality. 

But  why  should  not  such  a  basic  construct  as  the  physical  concepts 
of  force  and  mass  have  at  least  the  merit  of  providing  a  foundation 
for  an  intellectual  edifice  of  preliminary  truths,  which,  like  all  that 
we  think  and  believe,  is  not  eternal,  but  with  which  we  can  live 
for  a  time?  What  distinguishes  science  from  idle  talk  is  not  the 
nature,  but  the  breadth,  of  its  foundation,  and  the  consistency  of  its 
structure. 

3.  We  cultivate  science  for  no  other  reason  than  that  we  cannot  live  without  inter- 
preting the  world  as  best  we  can. 


Chapter  17.     The  Six   Cardinal  Problems  of  the  Division  of 
Labor  Discussed  Individually 


a.     THE    OCCUPATION    OF    A    PERSON 

What  does  any  given  person  produce?  Official  occupational  guid- 
ance should  assign  to  each  one  the  activity  in  which  he  could  best 
serve  the  interests  of  the  state.  But  as  long  as  the  state  allows  free 
choice  in  the  matter  everyone  selects  the  occupational  that  he  likes 
best  among  those  available  to  him.  In  so  far  as  his  liking  depends 
upon  earnings,  there  are  two  ways  of  deciding  on  an  occupation. 
One  is  the  marginal  view,  as  it  corresponds  to  the  Walrasian  method 
of  describing  equilibrium. 

§1.     The    Marginal   View 

The  marginal  approach  would  be  valid  if  "  labor  "  could  be 
subdivided  into  homogeneous  subgroups.  The  members  of  each 
subgroup  would  be  equally  good  at  every  occupation.  This  does  not 
mean,  however,  that  their  physical  productivities  need  be  com- 
parable. When  such  homogeneous  groups  exist,  the  following  equi- 
librium conditions  hold  true:  (1)  The  members  of  a  particular 
homogeneous  subgroup  are  distributed  among  the  various  industries 
in  such  a  way  that  their  wages  are  everywhere  the  same.  This  auto- 
matically also  gives  the  answer  to  the  question  just  put.  (2)  The 
members  of  the  different  groups  will  be  employed  in  such  numbers 
in  any  particular  industry  that  their  marginal  products  are  propor- 
tional to  their  wages.    This  also  answers  the  next  question. 

The  assumption  that  persons  can  be  divided  into  groups  within 
which  they  may  be  regarded  as  interchangeable  units  simplifies  the 
problem  greatly.  But  in  reality  it  is  improbable  that  even  two 
persons  would  be  equally  productive  in  one  and  the  same  activity, 
or  that  their  productivity  would  differ  in  the  same  proportion. 
This  means  the  impossibility  of  a  marginal  approach  that  would 
answer  our  question  summarily  for  whole  groups  of  persons.  But 
the  marginal  principle  could  be  applied  to  individual  persons  pro- 
vided they  were  units  large  enough  to  influence  wages  in  the  various 
activities.  For  then  a  person  would  divide  his  working  hours  among 

226 


The  Six  Problems  Discussed  Individually 


227 


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Part  Three.     Trade 


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Tlie  Six  Problems  Discussed  Individually 


229 


these  different  employments  according  to  the  principle  by  which 
the  group,  so  to  speak,  directs  its  members  into  the  individual 
branches.  But  since  the  individual  does  not  usually  exert  this 
influence  on  wages,  he  devotes  his  entire  time  to  the  trade  that  yields 
him  the  largest  return,  though  not  in  money  alone.  Thus,  with 
few  exceptions,  the  marginal  approach  fails  with  individuals  as  it 
does  with  groups. 

Table    77.    COMPARATIVE   EFFICIENCIES 
(COMPARATIVE  ADVANTAGES)   OF  THE   COUNTRIES" 


Country  I 

Country  II 

A 

B 

C 

D 

E 

F 

A 

B 

c 

D 

E 

F 

I 

100 

100 

100 

100 

100 

100 

125 

80 

175 

20 

60 

10 

II 

80 

125 

57 

500 

167 

1000 

100 

100 

100 

100 

100 

100 

III 

90 

37 

131 

100 

50 

100 

112 

30 

250 

20 

30 

10 

IV 

90 

25 

43 

100 

166 

950 

112 

20 

75 

20 

99 

95 

Country  III 

Country  IV          | 

A 

B 

C 

D 

E 

F 

A 

B 

C 

D 

E 

F 

I 

111 

265 

70 

100 

200 

100 

111 

400 

232 

100 

61 

10 

II 

89 

333 

40 

500 

333 

1000 

89 

500 

133 

500 

101 

105 

III 

100 

100 

100 

100 

100 

100 

100 

150 

233 

100 

30 

10 

IV 

100 

66 

30 

100 

333 

950 

100 

100 

100 

100 

100 

100 

*  Calcula 

ted  frc 

m  column  2  of  Tal 

Die  9. 

§2.     The    Principle   of   Comparative   Cost 

In  my  judgment  the  choice  of  an  occupation  follows  the  prin- 
ciple that  the  earlier  theory  of  international  trade  developed  for 
determining  the  international  division  of  labor:  the  principle  of 
comparative  cost.  As  a  matter  of  fact,  for  reasons  that  will  be  given 
in  discussing  the  fifth  problem,  this  principle  is  applicable  in  general 
only  to  persons,  not  to  countries.  As  it  is  more  familiar  to  us  in  its 
unwarranted  application,  however,  a  comparison  of  the  phenomena 
that  correspond  to  each  other  in  the  two  cases  may  be  of  interest.' 
But  first  the  application  of  this  principle  to  more  complicated  cases 
must  be  examined  in  greater  detail  than  it  has  been  in  the  literature 
heretofore.-  Althous;h  it  is  incorrect  to  do  so,  we  base  the  discussion 


1.  Of  course  its  application  to  the  division  of  labor  among  individual  persons  is 
not  new.  See  J.  D.  Black  (Introduction  to  Production  Economics  [New  York,  1926],  pp. 
129  ff.)  and  G.  von  Haberler  {Der  Internationale  Handel  [Berlin,  1933],  p.  100;  English 
edition  [1936],  pp.  130-131)  .  But  so  far  it  has  not  been  carried  through  accurately  or 
exhaustively  enough. 

2.  The  following  is  based  upon  my  article  on  comparative  cost,  "  Wo  gilt  das 
Theorem   der  komparativen   Kosten?  "    WeltwirtschaftUches  Archiv,  July,    1938.     (The 


ago  Part  Three.     Trade 

on  trade  between  countries  because  the  theory  will  be  familiar  to 
most  readers  only  in  this  connection. 

a.  Development  of  the  Principle 

Consider  first  only  two  countries.  So  long  as  the  number  of 
products  also  is  limited  to  two,  what  each  country  specializes  in 
can  be  unequivocally  determined  in  the  usual  way  from  differences 
in  comparative  cost.  If  there  are  several  products  we  can  only  give 
for  each  country  the  order  in  which  they  must  enter  international 
trade.  Only  with  the  help  of  the  additional  principle  of  fair  settle- 
ment of  the  balance  of  payment  (p.  298)  is  it  possible  to  decide  which 
goods  in  the  series  are  imported  and  which  are  exported.  If  the 
products  are  arranged  in  order  of  their  comparative  advantage 
beginning  with  the  good  in  which  country  I  has  the  greatest  com- 
parative advantage  over  country  II,  country  I  will  export  all  goods 
above  the  dividing  line  and  import  the  remainder.^  With  several 
products  and  more  than  two  producers,  the  sequence  of  comparative 
advantages  must  be  determined  separately  for  each  pair  of  countries. 
When  II  is  its  partner,  the  order  of  comparative  advantage  of 
country  I  differs  from  what  it  is  when  III  is  its  partner.  If  there  is 
trade  in  both  directions  between  two  countries,  I  and  II,  for 
example,  which  now  is  no  longer  necessary,  the  interchange  need 
not  extend  to  all  products  even  when  freight  costs  are  disregarded. 
On  the  contrary  there  are  then  two  dividing  lines  as  a  rule;  one 
below  the  exported  product  for  which  country  I  has  the  smallest 
comparative  advantage  over  II  (line  1) ,  and  one  above  the  corre- 
sponding product  exported  from  II  (line  2) .  Line  1  must  of  neces- 
sity lie  above  line  2.  Again  the  lines  are  determined  by  the  condition 
that  the  balance  of  payment  must  be  in  equilibrium.  But  if  the 
lines  for  only  one  pair  of  countries  are  available,  it  is  certain  only 
that  I  imports  everything  under  line  1  but  not  that  it  exports 
everything  above  it.  Similarly,  II  imports  everything  above  line  2 
but  does  not  export-  everything  below  it.    Hence  it  remains  un- 


erroneous  changes  introduced  by  the  editor  are  here  corrected.)    An  elementary  knowl- 
edge is  assumed. 

3.  The  dividing  line  can  be  determined  only  if  absolute  prices,  i.  e.,  the  price  level, 
as  well  as  relative  prices  implied  in  comparative  cost  are  given.  The  change  in  the 
price  level  has  the  function  of  restoring  equilibrium  in  the  balances  of  payments.  With 
a  gold  standard  the  price  levels  are  moved  back  and  forth  until  the  direction  and 
magnitude  of  the  absolute  price  differences  suffice  to  bring  the  international  accounts 
into  equilibrium  without  defaults  or  involuntary  credits.  Only  this  mechanism  trans- 
forms the  possible  (comparative)  into  real  (absolute)  cost  differences  in  sufficient 
numbers  and  in  order  of  their  magnitude. 


Tlie  Six  Problems  Discussed  Individually 


231 


decided  what  goods  enter  into  trade  between  the  two  countries. 
Only  for  commodities  lying  between  the  two  lines  is  it  true  without 
limitation  that  both  countries  will  import  them  from  other  countries. 
As  for  exports,  even  this  incomplete  knowledge  is  impossible.  It  is 
not  known  what  products  will  be  exported,  or  in  what  order  their 
chances  of  exportation  are  greatest. 

Tables  11  and  12,  calculated  from  Table  9,  will  serve  as  an 
illustration.  There  happens  to  be  only  one  dividing  line  for  trade 
between  I  and  every  other  country,  but  in  all  other  cases  there  are 
two.    Consider  the  trade  between  countries  11  and  III    (column  4, 


Table   12.   ORDER   OF   COMPARATIVE 
ADVANTAGES^ 


I 


I 


I 


II 


II 


III 


A 


E 


D     • 

F 


C     ^»      B      f»^§.B      f  ti     F 
C        •      D 
A 
D 
E 


B 
•      D 


•  c 

B 

•  A 


F      • 

E 
A 


II 


III 


IV 


III 


IV 


IV 


a.  Products  are  arranged  in  descending  order  of  advan- 
tages, taken  from  Table  II,  for  the  upper  row  of  countries  as 
compared  with  those  in  the  lower  row.  The  dots  and  arrows 
indicate  products  and  the  direction  of  exchange  between  two 
countries. 

Table  12) ,  for  example.  Line  1  lies  between  products  D  and  E, 
line  2  between  B  and  A.  Of  the  products  above  line  1,  country  II 
exports  food  D  to  country  III  but  not  food  F,  although  in  II  its 
comparative  advantage  as  compared  with  country  III  would  be  still 
greater.  But  in  comparison  with  country  IV  it  is  smaller,  with  the 
result  that  not  only  the  two  products  B  and  E,  lying  between  the 
dividing  lines,  but  also  F,  above  the  upper  line,  will  be  imported 
by  both  countries  from  a  third. 

We  summarize  what  may  be  concluded  from  a  simple  knowledge 
of  comparative  cost  in  the  three  cases  (two  countries— two  products; 
two  countries— many  products;  and  many  countries— many  products): 
In  the  first,  the  textbook  example  of  theory,  there  is  a  unique  line 
separating  imported  and  exported  goods.    In  the  second,  the  neces- 


232 


Part  Three.     Trade 


sary  sequence  in  which  goods  enter  international  trade  can  be  deter- 
mined, from  which  follows  the  hypothetical  proposition  that  if  the 
dividing  line  were  given  it  would  sharply  separate  imported  and 
exported  products.  The  third  case  provides  the  half-knowledge 
that  if  there  are  any  dividing  lines  at  all,  goods  on  the  farther  side 
of  the  line  would  all  be  on  the  list  of  imports  but  would  not  exhaust 
it.  From  this  follows  the  little  that  is  definitely  known  about  the 
trade  relationships  between  any  two  countries:  That  they  do  not 
exchange  the  goods  between  the  dividing  lines  but  import  them 
from  this  and  other  countries.  Whereas  everything  is  known  in  the 
second  case,  once  the  dividing  line  is  given,  in  the  third  case  even 
the  lines  separating  two  countries  provide  only  partial  information 
as  to  what  takes  place  between  them.  For  a  full  knowledge  of  the 
trade  between  even  two  countries  we  need,  in  addition,  the  dividing 
lines  between  the  two  in  question  and  all  others.  Thus  in  the  case 
of  several  goods,  and  even  more  so  in  the  case  of  several  countries, 
it  is  very  hard  to  determine  what  a  country  will  export;  this  cannot 
be  decided  from  comparative  cost  alone,  without  the  additional 
principle  of  the  fair  settlement  of  balances  of  payment;  and  with 
more  than  two  countries  we  require  a  knowledge  of  the  trade  of 
the  other  countries  as  well,* 

/?.    Application  of  the  Principle  of  Comparative  Cost  to  the 
Choice  of  an  Occupation 

Now  compare  trade  between  countries  and  trade  between  per- 
sons, in  order  to  see  what  concepts  of  interpersonal  trade  correspond 
to  those  with  which  we  are  already  familiar  from  international  trade 
(Tables  9  and  10) .  For  this  purpose  we  must  proceed  as  though 
the  principle  actually  could  be  applied  to  foreign  trade.  A  scale  of 
relative  productivity  can  be  set  up  for  a  person  exactly  as  for  a 
country    (column  2)  .°    From  these  proportionality  coefficients  and 

4.  The  matter  may  be  expressed  in  this  way  also:  The  principle  of  comparative  cost 
is  valid  between  two  countries,  but  it  is  impossible  to  determine  by  a  comparison  of 
costs  between  these  two  alone  what  they  will  exchange  with  one  another,  in  which 
direction,  and  with  what  probability.  Other  countries  and  the  rate  of  exchange  so 
interfere  with  the  system  as  to  make  it  possible  to  say  in  advance  only  that  the  order 
in  which  goods  are  exchanged  between  two  countries,  which  is  fixed  by  the  size  of 
comparative  advantages,  can  be  interrupted  but  not  jumbled. 

5.  The  following  derivation  assumes  that  efficiency  remains  constant.  I  have 
endeavored  to  show  elsewhere  that  the  principle  of  comparative  cost  holds  at  the 
margin  also  when,  as  with  factory  workers,  efficiency  varies  with  employment  in  the 
firm.  ("  Wo  gilt  das  Theorem  der  komparativen  Kosten?  "  Weltioirtschaftliches  Archiv, 
July,  1938,  pp.  50-52). 


The  Six  Problems  Discussed  Individually  233 

the  absolute  output  of  one  of  the  producers  in  a  unit  of  time 

(column  3)  the  national  price  system  before  entrance  into  inter- 
national trade  can  be  calculated  (Column  4  of  Table  9  contains  in 
addition  the  absolute  level  of  prices  in  domestic  currencies,  and 
thus  involves  a  further  assumption  about  the  quantity  of  money) , 

In  exactly  the  same  way,  the  goods  that  the  individual  produces 
exchange  in  proportion  to  the  working  time  spent  on  them   (Table 

10,  column  4) . 

In  both  cases,  finally,  we  need  a  rate  of  exchange  to  convert  the 
domestic  unit  of  account  (reichmarks,  hours)  into  a  foreign  unit 
in  which  all  domestic  prices  are  then  comparable.  For  countries 
this  international  unit  might  be,  for  example,  the  pound  sterling 
or  gold;  for  individuals  it  is  the  standard  currency  (say  reichsmarks) . 
This  exchange  ratio  fixes  the  relative  height  of  the  domestic  price 
level.  It  is  familiar  to  us  in  international  trade  as  the  rate  of  ex- 
change, and  the  hourly  wage  in  interpersonal  trade  corresponds  with 
it  almost  to  a  hair.*^  Just  as  a  national  unit  of  value  like  the  reichs- 
mark  can  be  converted  into  an  international  unit  like  the  pound 
sterling  by  means  of  the  exchange  rate  (Table  9,  column  3),  so  the 
personal  unit  of  value,  the  hour,  can  be  converted  into  the  general 
unit,  the  reichsmark,  by  means  of  the  hourly  wage  (Table  10,  column 
5).  The  level  of  the  exchange  rate  depends  upon  reciprocal  demand, 
and  should  bring  this  into  equilibrium.  As  with  countries,  so  with 
individuals;  the  sum  of  their  debits  must  equal  the  sum  of  their 
credits;  that  is,  their  balance  of  payments  must  be  in  equilibrium. 
And  in  the  absence  of  a  knowledge  of  demand  relationships  the 
rates  of  exchange  in  both  cases  can  be  assumed  arbitrarily  only 
within  certain  limits.^  They  must  always  be  such  that  no  product 
is  excluded  from  interchange;  otherwise  equilibrium  would  not 
prevail.  The  producer  with  a  rate  of  exchange  that  was  too  high 
would  lower  his  rate,  or  his  wage  demands,  as  the  case  might  be, 
until  even  he  could  produce  at  least  one  article  more  cheaply  than 
the  others. 

And  now  we  come  to  the  sole  difference,  a  difference  in  degree. 
In  the  international  division  of  labor  an  article  can  be  produced  in 
several  countries  if  none  of  them  alone  can  wholly  satisfy  world 
demand.  Conversely,  countries  may  be  so  large  that  they  are  able 
to  export  more  than  one  product.    The  latter  is  not  generally  true 

6.  The  sole  difference  is  ttiat  tfie  excfiange  rate  does  not  give  tlie  international  wage 
for  a  working  hour  directly,  but  only  after  the  introduction  of  an  intermediate  link 

(the  hourly  wage  in  national  currency) . 

7.  See  G.  von  Haberler;  Der  internaiionale  Handel   (Berlin,  1933) ,  p.  102;  English 
edition   (1936) ,  p.  133. 


20J  Part  Three.     Trade 

of  persons.  The  demand  for  most  goods  is  so  great  that  no  one 
individual  alone  can  fully  meet  it,  much  less  engage  in  several  occu- 
pations at  the  same  time.^  Thus  in  setting  the  hourly  wage  in 
Table  10  we  must  be  sure  not  only  that  each  worker  can  engage  in 
one  trade,  but  also  that  the  efficiency  wage  corresponds  for  all  equals 
in  a  trade.  Thus  whereas  farm  laborer  III  in  Table  10  receives  an 
hourly  wage  of  but  66  cents  and  farm  laborer  I  is  paid  $1.10,  they 
are  rewarded  exactly  according  to  their  productivity.  The  wage  for 
one  unit  and  the  price  for  one  unit  are  the  same  everywhere,  no 
matter  what  person  or  what  country  supplies  the  unit.  If  we  had 
assumed  for  countries  also  that  no  individual  country  could  by 
itself  satisfy  world  demand,  we  should  have  had  to  take  into  account, 
in  determining  the  exchange  rate,  the  condition  that  prices  of  the 
same  commodity  must  be  equal  in  different  countries.  Efficiency 
wages  and  international  prices  correspond  to  each  other. 

To  elucidate  this  perfect  correspondence  further  we  shall  now 
discuss  the  effect  of  a  few  disturbing  elements,  the  main  subject  of 
the  theory  of  international  trade,  under  simple  assumptions  in 
interpersonal  trade.  Suppose  that  a  man  is  willing  to  work  for  a 
very  low  hourly  wage,  which  correspond  to  dumping  by  a  country. 
Several  different  jobs  are  offered  him;  everyone  attempts  to  employ 
him,  and  the  demand  exceeds  his  capacity  for  work.  He  finds  that 
he  can  ask  a  higher  hourly  wage  and  still  be  fully  employed.  As 
his  demands  increase  he  eliminates  more  and  more  possibilities, 
until  his  wage  demands  at  last  are  so  high  that  his  efficiency  in  but 
one  single  trade  corresponds  to  it.  This  one  he  chooses.  In  the  same 
way  international  cut-throat  competition,  too,  finally  reaches  its 
limits  and  its  legitimate  place.  However,  with  a  very  large  country 
it  takes  longer  to  reach  the  point  where  the  demand  for  its  goods 
exceeds  productive  capacity  and  drives  its  exchange  rate  upward, 
until  the  foreign  demand  for  its  still  remaining  special  products  can 
be  satisfied  by  the  domestic  supply  of  hours  of  work  required  to 
produce  them.  Sooner  or  later  this  point  must  be  reached.  Hourly 
wage  and  exchange  rate  will  finally  become  so  high  that  the  balance 

8.  There  are  exceptions;  for  example,  among  sparse  populations.  There  the  hourly 
wage  is  so  adjusted  that  the  sum  of  the  activities  possible  at  this  wage  just  fill  the 
working  time  of  a  man.  Consider  the  versatility  of  the  rural  artisan,  or  the  combina- 
tion of  innkeeping  with  agriculture;  a  sharp  separation  of  occupations  would  be 
undesirable  in  rural  districts.  Secondly,  the  wish  to  be  continuously  employed  forms 
one  of  the  main  reasons  for  the  existence  of  the  farmer-workman.  Because  of  its 
fluctuations  industry  cannot  employ  labor  constantly  throughout  the  year,  and  agri- 
culture is  carried  on,  therefore,  as  a  side  line.  Hence  the  difference  between  personal 
and  international  trade  is  one  of  degree  only. 


The  Six  Problems  Discussed  Individually  235 

of  payments  is  equalized  in  both  cases;  that  is,  the  national  or 
personal  supply  of  working  hours  times  their  price  (=  export)  is 
equal  to  the  demand  for  foreign  goods   (==  import) . 

Another  example  of  the  difference  in  degree  mentioned  above: 
In  order  to  pay  debts  out  of  current  income,  a  country  must  lower 
its  prices,  and  this  increases  its  export  surplus,  partly  through 
increased  exports  and  partly  through  decreased  imports.  An  indi- 
vidual (a  wage  earner) ,  on  the  other  hand,  does  not  generally  have 
to  lower  his  price  in  order  to  increase  his  "  export,"  since  he  exports 
his  entire  production  anyhow  and  exerts  no  influence  on  its  price. 
He  cannot  raise  his  income  by  undercutting,  but  only  by  working 
more  hours.  Of  course  the  normal  way  of  achieving  the  necessary 
export  surplus  is  for  him  to  cut  down  his  expenditures,  which  again 
requires  no  lowering  of  "  domestic  prices."  A  typical  example  of 
transfer  by  a  simple  shift  in  buying  power  without  change  of  price! 
It  is  based  upon  the  relative  insignificance  of  the  individual  in  the 
whole  economy. 

The  table  summarizes  this  one-to-one  correspondence 
between  international  and  interpersonal  trade 

INTERNATIONAL  TRADE  INTERPERSONAL  TRADE 

Rates  of  exchange  Hourly  wages 

International  prices  Efficiency  wages 

Barter  terms  (relation  of  export  to  Real  wages  (relation  of  wages  to  prices 

import  price)  of  goods) 

National  price  system  Relation  of  time  spent  per  unit 

National  price  level  Wage  level 

Gold  import  Hoarding  (hiding  money  in  a  stocking) 

Capital  export  Saving   (depositing  money  in  a  bank) 

Export  =  import  Earnings  =  purchases 

The  question,  upon  what  does  a  rational  choice  of  an  occupation 
depend,  may  therefore  be  answered  to  this  effect  in  so  far  as  it 
depends  on  earnings:  upon  the  native  aptitude  of  a  person;  upon 
the  price  he  can  get,  and  upon  the  length  of  the  workday.  These 
determine  the  highest  hourly  wage  that  will  just  ensure  his  full- 
time  employment.  Thus  the  choice  of  an  occupation  does  not 
depend  simply  upon  aptitude  but  upon  how  much  it  will  bring  in 
and  how  much  employment  it  will  provide.  This  formulation  is 
especially  valid  for  the  case  of  a  limited  monopoly,  which  enables 
one  to  engage  in  several  activities  and  to  influence  their  prices.  As 
long  as  full-time  employment  in  one  occupation  is  possible,  the 
matter  may  also  be  put  in  this  way:  That  occupation  will  be  chosen 
which  pays  the  highest  hourly  wage  considering  aptitude  and  effi- 
ciency wages.    The  parallel  with  international  trade  is  complete. 


236  Part  Three.     Trade 

What  a  country  will  eventually  export  or  a  person  produce  in  his 
occupation  depends,  with  given  comparative  advantages,  upon  the 
exchange  rate  that  each  achieves  in  equilibrium.  Both  will  specialize 
in  what,  compared  at  this  exchange  rate,  they  can  produce  at  least 
as  cheaply  as  others.  Thus  exchange  rate  and  hourly  wage  have 
exactly  the  same  function. 

But  the  choice  of  an  occupation  does  not  depend  entirely  on 
money  income,  as  we  have  been  assuming  up  to  now,  or  even  upon 
the  utilities  that  this  income  will  buy.  On  the  contrary,  to  these 
more  or  less  variable  utilities  there  must  be  added  all  those  impon- 
derables that  are  associated  with  various  occupations  and  usually 
appear  as  fixed  utilities  (or  disutilities) .  For  a  man  aims  at  the 
highest  total  utility,  not  at  the  highest  purchasable  utility,  but  the 
general  principles  for  making  his  decisions  are  the  same  for  the 
utility  calculus  as  for  the  money  calculus.  When  engaged  in  several 
trades  at  once,  he  will  work  at  them  and  apportion  his  time  among 
them  until  the  utility  per  time  unit  is  the  same  at  the  margin  for 
all  activities  and  equal  to  the  marginal  cost  (measured  in  disutilities 
or  in  other  utilities  relinquished) .  The  principle  of  comparative 
cost,  too,  is  probably  applicable  to  the  utility  calculus,  even  though 
with  difficulty. 

b.     THE    PERSONNEL    OF    AN    INDUSTRY 
§1.     The    Personnel   of   an  Occupation 

What  have  the  members  of  any  given  occupation  in  common? 
First,  this:  that  despite  all  difficulties  they  are  equal  to  the  demands 
made  upon  them.  This  may  presuppose  a  certain  minimum  of 
aptitudes  that  is  more  or  less  rare,  depending  on  the  kind  and 
quality  of  work.^  In  any  case  this  common  characteristic  (at  least 
as  far  as  native  ability  to  perform  the  jobs  is  concerned)  is  not 
restricted  to  members  of  a  particular  occupation.  The  particular 
ability  may  be  found  outside  the  occupation  to  a  greater  or  lesser 
degree.  It  can  therefore  be  at  most  a  necessary  characteristic,  which, 
moreover,  hardly  need  be  mentioned.  It  is  never  a  sufficient  charac- 
teristic. Is  not  the  relevant  question  for  the  members  of  an  occupa- 
tion how  quickly  the  job  can  be  done,  rather  than  whether  it  can  be 

9.  It  may  even  presuppose  a  definite  type  of  man.  The  dextrous  textile  worker, 
for  example,  tends  to  be  an  extrovert,  the  steadier  mine  or  foundry  worker  an  introvert 
(W.  Mitze,  Die  strukturtypologische  Gliederung  einer  westdeutschen  Grosstadt  [Leipzig, 
1941]) .  A  distinction  should  be  drawn,  of  course,  between  how  much  this  is  a  cause 
of  the  choice  of  a  trade  and  to  what  extent  it  is  a  result. 


The  Six  Froblctns  Discussed  Individually  237 

done  at  all?  What  is  the  exact  meaning  of  the  formula  that  says  there 
are  found  in  an  occupation  all  those  who  are  "  relatively  most  pro- 
ductive "  in  it,  or  who  are  "  comparatively  superior  "  ?  In  no  case 
can  it  inean  those  who  objectively  produce  most  in  it  as  compared 
with  other  persons.  A  bank  president  will  not  change  places  with  a 
bootblack  because  he  excels  him  in  polishing  shoes,  as  well  as  in 
banking.  But  neither  can  the  formula  mean  those  who  come  nearest 
to  the  world  record  in  this  special  occupation;  that  is,  those  who 
are  subjectively  most  skillful  in  it.^°  In  Table  10,  for  example,  a  II 
chooses  occupation  D,  where  his  output  is  60  per  cent  of  the  world 
record,  not  occupation  A,  where  it  is  80  per  cent,  for  the  simple 
reason  that,  considering  the  pay  in  both,  his  hourly  wage  is  greater 
in  D.  Or,  more  obviously,  a  banker  may  be  a  superb  messenger 
but  a  second-rate  bank  president.  Yet  he  earns  more  as  a  president 
when  he  multiplies  his  output  by  the  efficiency  wage. 

But  what  else  can  the  phrase  "  comparatively  superior  "  mean? 
As  in  international  trade,  it  can  be  applied  only  to  two  producers. 
If  their  relative  productivity  in  various  occupations  is  arranged  in 
series,  each  will  choose  an  occupation  on  that  end  of  the  series 
which  is  more  favorable  for  him.  Exactly  what  this  is  can  be  deter- 
mined only  if  the  equilibrium  wage  of  all  producers  is  known. 
Then  it  will  appear  that  all  who  choose  a  given  occupation  have  in 
common  only  that  they  earn  most  in  it  and  that  this  occupation, 
when  compared  with  any  given  persons  in  another  occupation,  is 
on  that  end  of  the  comparative  series  which  is  more  favorable  for 
them.  The  formula  for  comparatice  advantage,  so  clear  in  simple 
cases,  is  both  obscure  and  incomplete  in  complicated  ones.  In  any 
case,  it  is  not  necessarily  the  most  skillful  in  any  ordinary  sense 
who  gather  together  in  an  occupation, '^'^  but  those  whose  produc- 
tivity in  it  is  at  least  so  great  that  it  earns  them,  and  them  alone, 
the  highest  hourly  wage  at  the  prevailing  piece  wage.^-    Or,  stated 

10.  Except,  perhaps,  in  the  case  of  two  men  only,  where  "  most  skillful  subjectively  " 
is  the  same  as  "  comparatively  superior." 

11.  This  leads  to  doubts  whether  Schumpeter  is  correct  when  he  sees  in  special 
aptitudes  for  definite  functions  the  origin  of  class  differences.  (J.  A.  Schumpeter,  "  Die 
sozialen  Klassen  im  ethnisch  homogenen  Milieu,"  Archiv  fiir  Soziahvissenschaft,  1927, 
pp.  1-67,  particularly  p.  58.)  Only  when  wages  are  paid  by  time  rather  than  by  output 
is  it  true  that  with  rational  selection  no  one  performing  a  definite  task  is  sufficiently 
qualified  for  a  more  highly  paid  one.    See  p.  240. 

12.  What  follows  from  this  for  the  choice  of  an  occupation  by  women?  That  women 
are  as  efficient  as  men  in  many  occupations  was  once  an  effective  argument  in  the 
feminist  movement.  But  it  was  sound  only  when  wages  were  paid  according  to  time, 
not  to  efficiency.  Otherwise  it  is  irrelevant  in  the  choice  of  a  suitable  occupation 
whether  the  absolute  output  of  women  is  equal  to  that  of  their  male  associates.    The 


238  Part  Three.     Trade 

Still  more  generally,  when  one  leaves  the  money  for  the  utility 
calculus:  As  against  outsiders,  the  members  of  any  given  occupation 
have  only  one  thing  in  common:  they  find  their  highest  satisfaction 
in  it." 

A  few  examples  will  perhaps  clarify  this  point.  Among  all 
workers  in  occupation  D  (Table  10) ,  81  is  most  and  all  least  skillful. 
Hence  their  hourly  wages  are  $1.00  and  60  cents  respectively.  If  the 
wage  for  piecework  should  fall  from  10  to  8.5  cents  per  unit  both 
would  leave  the  occupation  because  they  could  earn  more  elsewhere 
(81  in  C,  csll  in  A) .  Or  again:  A  rise  in  the  piece  wage  in  occupation 
B  from  78  to  84  cents  will  attract  not  only  worker  ^I,  who  is 
unexcelled  in  this  trade,  but  the  moderately  skillful  jSlII  also.  It  is 
thus  impossible  to  say  in  advance  who  will  be  the  marginal  worker 
when  wages  rise.  It  need  not  even  be  the  one  who  is  least  efficient 
in  this  occupation;  indeed,  the  most  skillful  worker  may  only  now 
enter  the  occupation  because  he  has  nevertheless  earned  more  until 
then  in  another;  and  it  is  even  possible  that  the  most  efficient  worker 
will  leave  an  occupation  because  in  the  future  he  will  earn  more 
elsewhere.  The  marginal  worker  in  an  occupation  is  therefore  one 
whose  hourly  wage  in  another  most  nearly  approaches  his  earnings 
at  the  occupation  in  question.  Or,  in  brief:  The  marginal  producer 
is  not  the  worst,  but  the  most  unwilling  producer. 

Although  workers  in  every  employment  can  be  arranged  in  order 
of  productivity,  this  does  not  exclude  the  fact  that  there  are  persons 
engaged  in  other  employments  who  could  be  included  in  this  one, 
not  only  at  the  end  of  the  productivity  series  but  anywhere  along 
the  scale,  some  of  whom  could  be  drawn  in  by  higher  wages.^* 


most  lucrative  occupation  for  a  woman  is  at  the  same  time  necessarily  one  in  which 
she  is  comparatively  superior  to  all  men  who  pursue  another  one,  and  perhaps  even 
absolutely  superior  to  some  of  them;  the  latter,  however,  is  not  necessary.  On  the 
contrary,  an  activity  in  which  a  woman  surpasses  all  men  may  earn  her  less  than 
another  in  which  she  is  absolutely  inferior  to  all  men.  Hence  "  typical  women's  occu- 
pations "  can  be  described  only  as  the  ones  in  which  those  who  earn  the  most  are 
generally  women.  These  women  are  comparatively  superior  in  it  to  all  men;  that  is 
to  say,  they  do  this  work  relatively  better  than  they  would  do  "  men's  work."  But  it 
would  not  be  to  the  advantage  of  all  women  who  might  be  comparatively  superior  to 
men  in  this  occupation  to  enter  it.  The  relation  between  aptitude  and  the  choice  of 
an  occupation  is  by  no  means  so  simple. 

13.  That  is,  thevhlghest  satisfaction  possible  for  them  under  existing  conditions. 

14.  Thus  the  wage  in  a  given  employment  does  not  depend  upon  the  productivity 
of  the  least  efficient  though  still  necessary  worker,  but  upon  how  many  believe  it  most 
advantageous  to  specialize  in  such  work  at  this  particular  wage  within  a  given  wage 
structure.  From  this  must  be  distinguished  the  case  in  which  the  productivity  of  the 
marginal  worker  is  reduced,  not  because  of  his  personal  inefficiency  but  for  reasons 


The  Six  Problems  Discussed  IndividuaUx  239 

The  entrepreneur  is  interested  chiefly  in  the  wage  per  unit  ^^ 
of  output,  the  worker  only  in  his  hourly  wage.  Mistaken  kindness 
toward  labor  has  made  the  latter  into  the  wage;  that  is,  the  price 
of  the  worker's  output.  Payment  by  time  instead  of  by  output  has 
revolutionary  results:  AVith  a  piece  wage  there  are  no  "  better  paid  " 
occupations,  because  there  is  no  basis  for  comparison.  The  wage 
for  making  a  coat  cannot  be  compared  with  that  for  making  a  pair 
of  shoes.  Uniform  hourly  wages  for  tailors  and  cobblers  do  not 
exist  when  they  are  paid  according  to  output. 

The  picture  changes  when  wages  are  paid  according  to  fixed 
hourly  wage  schedules.  Many  who  would  have  earned  more  at  their 
former  occupations  under  free  competition  are  driven  into  more 
lucrative  ones,  where  they  are  still  worth  the  higher  wage  despite 
their  lower  productivity.  And  all  who  would  have  earned  less  under 
free  competition  are  driven  into  less  lucrative  occupations  as  long 
as  they  are  sufficiently  productive  there  to  earn  the  established  wage. 
The  others  join  the  ranks  of  the  unemployed.  Only  wage  schedules 
make  marginal  workers  economically  significant;  that  is,  marginal 
in  the  sense  of  the  least  productive  workers,  not  in  the  sense  given 
above  of  those  that  are  readiest  to  leave  or  to  enter  an  occupation. 
Only  in  the  case  of  wage  schedules  is  it  correct  to  say  that  all  those 
engaged  in  a  more  lucrative  occupation  are  objectively  more  pro- 
ductive in  it  than  all  in  less  lucrative  ones.  The  situation  differs 
fundamentally  from  barter,  where  it  need  not  be  true  that  those 
who  objectively  or  subjectively  excel  in  a  task  will  actually  perform 
it  also.  When  wages  are  determined  in  a  free  market  that  occu- 
pation will  be  chosen  that  will  lead  to  the  highest  earnings  when 
efficiency  and  piece  rates  are  taken  into  account.  With  an  hourly 
wage  schedule  that  occupation  is  chosen  in  which  output  times  the 
piece  rate  is  at  least  equal  to  the  established  hourly  wage  and  which 
offers  the  highest  hourly  wage  of  all.  (This  is  true  only  when  wages 
are  determined  in  a  free  market.)  Of  course,  it  is  not  necessary  that 
output  times  the  piece  rate  should  equal  any  of  the  existing  time 
rates.  This  will  then  result  in  the  army  of  unemployed  that  muddled 
philanthropists  are  never  tired  of  creating. 


connected  with  the  organization  of  the  firm;  for  example,  because  the  firm  has 
exceeded  its  optimum  size  or  is  being  run  by  a  marginal  entrepreneur  whose  incom- 
petence impairs  the  work  of  his  employees.  Though  the  marginal  view  has  become 
impossible  from  the  standpoint  of  the  individual  person,  it  remains  valid  from  the 
standpoint  of  industry.  It  will  continue  to  attract  a  mixed  group  of  persons  of  all 
degrees  of  efficiency  until  the  value  of  the  marginal  product  equals  the  wage  paid  for  it. 
15.  Except  in  so  far  as  production  results  in  costs  that  depend  simply  upon  the 
lapse  of  time  or  upon  the  duration  of  the  production  process.  Then  he  also  is  inter- 
ested in  work  tempo  and  hence  in  the  hourly  wage  of  the  individual  worker. 


240 


Part  Three.     Trade 


§2.     The   Personnel   of   a   Firm 

Who  works  at  the  production  of  a  given  commodity?  At  bottom 
the  answer  is  the  same  as  that  to  the  question  discussed  in  the  pre- 
ceding section,  except  that  here  it  is  even  more  manifest  that  highest 
utility  rather  than,  say,  similar  characteristics,  leads  persons  into 
the  same  firm.  This  follows  from  the  multiplicity  of  occupations 
represented  in  a  firm;  all  that  has  been  said  previously  holds  true 
for  members  of  the  same  occupation,  but  we  must  at  least  touch 
upon  an  additional  point.  The  preceding  analysis  implied  that  in 
free  occupations  all  persons  produce  independently  as  master  crafts- 
men, dealers,  or  farmers.  At  the  least  it  implied  that  the  combination 
of  workers  in  firms  does  not  affect  their  productivity.  Whenever  this 
assumption  is  not  valid  the  choice  of  an  occupation  does  not  depend 
upon  different  efficiencies  in  themselves  (which  in  many  occupations 
are  not  even  conceivable) ,  but  upon  different  possibilities  for  pro- 
duction, which  depend  on  combinations  with  other  factors  of  pro- 
duction possible  at  any  moment.  These  are  a  function  of  the  degree 
of  utilization  of  the  capacities  of  a  plant  at  any  given  time.  Thus 
the  choice  of  an  occupation  by  employed  workers  depends  still  less 
upon  mere  aptitude  than  does  that  by  the  self-employed.  On  the 
contrary,  the  common  output  of  persons  in  different  occupations,  as 
represented  in  a  factory,  is  also  a  function  of  the  price  of  their 
products  and  the  technical  possibilities  at  any  one  time  for  devel- 
oping aptitudes. 

c.     THE    LOCALITY    OF    A    PERSON 

Where  does  any  given  man  produce?  This  time  we  shall  invert 
our  customary  procedure  and  trace  our  answer  step  by  step  from 
special  to  more  general  solutions. 

§1.     The   Locality    of   Employed   Workers 

a.    Equal  Nominal  Wages 

All  popular  views  on  a  person's  choice  of  location  agree  on  one 
point:  the  principle  of  interlocal  equalization  of  the  wage  level. 
Only  against  this  background  is  it  possible  to  understand  the 
shocking  opinion  of  the  American  Department  of  Labor  given  to 
the  NRA,  which  declared  local  wage  differentials  economically 
unjustifiable.  This  view  could  be  defended  on  two  assumptions, 
of  which  one  is  not  given  in  reality  and  the  other  is  not  desirable. 


The  Six  Problems  Discussed  Individually  241 

1.  There  is  in  fact  a  dangerous  modern  tendency  toward  the 
inter-local  equalization  of  nominal  wages.  Its  supporters  are  those 
who  are  either  unwilling  or  unable  to  perceive  differences  in  places 
and  things,  and  in  this  and  in  other  matters  follow  what  others  do 
without  considering  reasons  for  and  against.  They  follow  the  highest 
nominal  wage  as  though  it  were  a  magnet.  These  persons,  who 
consider  only  the  money  wage,  tend  to  equalize  it  everywhere  if 
they  are  sufficiently  numerous. 

2.  If  the  "  iron  law  of  wages  "  held,  an  individual  would  work 
where  he  found  a  livelihood,  and  all  together  would  be  located  so 
that  as  many  persons  as  possible  could  live  on  this  planet,^''  But 
as  the  number  of  people,  unlike  the  number  of  firms,  does  not  tend 
to  reach  the  maximum  number  possible,  labor,  like  land,  receives 
a  scarcity  rent;  that  is,  the  workman  earns  more  than  his  cost  of 
reproduction.  Like  every  entrepreneur,  he  will  consequently  seek 
a  location  where  his  profit  will  be  greatest.  In  both  cases  profit  is 
the  difference  between  receipts  and  variable  costs,  both  of  which 
are  functions  of  location. ^^  With  persons  variable  costs  are  not  only 
the  expenses  necessary  to  mere  existence  (as  little  as  expenses  in 
a  firm  go  only  for  the  maintenance  of  capital  goods) ,  but  also 
such  additional  expenditures  beyond  mere  existence  as  keeping  fit 
for  work  with  better  food,  work  clothes,  carfare,  and  so  on.  But 
like  everyone  in  a  limited  monopolistic  position  the  individual  is 
free  to  choose  his  location  in  such  a  way  that  his  gain  accrues  not 
chiefly  in  money,  but  more  directly  in  some  such  natural  form  as 
a  more  agreeable  climate  instead  of  higher  wages.  From  this  it 
follows  most  emphatically  that  nominal  wages  can  never  be  equalized 
interlocally  any  more  than  they  can  be  equalized  among  occupations. 
'Man  wishes  to  maximize  his  total  utility,  not  only  his  monetary 
return.  But  interlocal  equalization  of  total  utilities  requires  inter- 
local inequality  of  nominal  wages;  that  is,  of  wages  for  piecework, 
since  the  hourly  wage  varies  in  any  case  for  different  persons,  as 
we  have  seen. 

fi.   Equal  Real  Wages 

It  will  be  objected,  however,  that  only  real  wages  for  piecework 
are  supposed  to  be  equalized.  But  that  again  is  not  correct.  For 
the  individual  the  difficulty  of  comparing  real  wages  interlocally 

16.  Mutatis  mutandis  this  statement  holds  also  for  firms,  in  so  far  as  they  are 
subject  to  an  "  iron  law  of  profits." 

17.  Only  in  statics  is  profit  the  difference  between  the  receipts  and  total  costs, 
because  here,  otherwise  than  in  dynamics,  the  probability  is  that  fixed  costs  too  will 
be  recovered. 


242  Pai^t  Three.     Trade 

might  be  overcome.  The  type  of  work  is  generally  different  in 
different  places,  and  when  his  place  of  residence  has  to  be  changed 
with  a  change  in  his  place  of  work  a  man  becomes  completely 
unsettled.  The  price  system,  and  accordingly  his  consumption 
pattern,  changes  from  place  to  place;  in  many  localities  he  will  be 
unable  to  procure  goods  to  which  he  has  become  accustomed  because 
their  possible  sales  areas  do  not  extend  that  far.^^  But  in  so  far  as 
his  marginal  utilities  change  with  relative  price  and  with  his  environ- 
ment he  will  voluntarily  ^^  adapt  himself  to  local  custom,  which 
R.  Wilbrandt  ^°  ingeniously  derives  from  the  local  marginal  utility, 
which  is  largely  fixed.  Thus  the  individual,  though  not  necessarily 
a  statistician,  could  in  principle  compare  the  utilities  purchasable 
in  various  places. 

But  our  total  satisfaction  does  not  depend  solely  upon  what  we 
can  buy  in  various  places  with  the  income  available  at  a  given  time. 
For  besides  purchasable  goods  unique  things  that  are  without  price 
influence  our  location;  those  individual  characteristics  of  places  and 
people  that  cannot  be  interchanged,  all  those  imponderables  of 
production  and  consumption  that  often  mean  incomparably  more 
to  us  than  the  economic  process  proper.  For  this  reason  potential 
real  wages  for  the  same  worker,  unlike  the  wholesale  price  for  the 
same  product,  may  differ  from  place  to  place  by  more  than  his 
travel  costs. 

y.   Equal  Satisfaction 

We  wish  to  maximize  neither  our  money  wage  nor  our  real  wage, 
but  our  total  utility.  This,  too,  differs  interlocally  for  individuals 
by  far  more  than  traveling  expenses,  for  it  makes  an  enormous 
difference  whether  we  were  born  in  a  place  or  have  to  move  there. 
Migration  means  relinquishing  much  that,  like  friends,  can  be 
replaced  only  after  a  long  time;  or  never,  like  one's  native  place. 
We  cannot  take  landscape  and  people  with  us.  And  seldom  do  we 
become  as  attached  to  new  surroundings  as  if  we  had  grown  up 

18.  In  his  admirable  study  L.  B.  Zapoleon  ("  International  and  Domestic  Com- 
modities and  the  Theory  of  Prices,"  Quarterly  Journal  of  Economics  XLV  [1931],  443) 
expresses  the  opinion,  however,  that  local  differences  in  the  style  of  living  nowadays 
show  more  in  the  relative  amounts  in  which  goods  and  qualities  obtainable  every- 
where are  bought,  than  in  the  existence  of  different  products  that  can  be  obtained 
only  locally. 

19.  On  the  other  hand,  those  local  differences  in  custom  to  which  one  adapts  oneself 
simply  in  order  not  to  seem  queer  can  no  longer  be  included  in  the  concept  of  real 
wages. 

20.  R.  Wilbrandt,  Vom  Leben  der  Wirtschaft,  P.  I    (Berlin,  1937)  . 


The  Six  Problems  Discussed  Individually  243 

among  them  and  were  wholly  a  part  of  them.  Hence  the  same  wage 
and  other  identical  circumstances  provide  a  newcomer  with  less 
utility  than  they  give  to  a  native  with  the  same  characteristics.  In 
the  marginal  case,  therefore,  utility  differs  interlocally  for  indi- 
viduals by  traveling  expenses  plus  the  loss  of  one's  home.^^-'* 

Are  there  any  other  universally  valid  interlocal  differences  in 
utility?  If  all  persons  were  alike,  and  if  they  chose  what  they  recog- 
nized as  an  improvement  over  their  present  activities,  total  utility 
would  again  differ  interlocally  at  most  by  traveling  expenses  and 
compensation  for  the  loss  of  one's  home.^^  But  as  no  interpersonal 
utility  comparison  can  be  drawn,  or  even  a  comparison  of  the  util- 
ities of  the  "  same  "  person  at  different  times  ^®— because,  to  put  it 
plainly,  the  concept  of  utility  is  nothing  but  a  chimera— spatial  com- 
parison of  utilities,  to  say  nothing  of  equalization,  is  impossible  in 
any  sense  at  all. 

21.  Thus  as  long  as  familiar  conditions  continue  to  exert  their  charm  and  expenses 
make  removal  difficult,  freedom  of  movement  will  not  lead  to  limitless  agglomeration. 

22.  If  a  person  could  divide  his  working  hours  and  his  free  time  among  several 
localities,  equalization  of  his  local  marginal  utilities  (after  deduction  of  traveling 
expenses  and  loss  of  his  home)   would  constitute  the  condition  of  equilibrium. 

23.  Hence  the  utility  that  must  be  offered  a  worker  in  order  to  induce  him  to 
change  his  place  of  employment  increases,  at  first  slowly,  with  the  distance  of  the  new 
location  from  his  original  home  (as  long  as  this  can  be  letained)  ;  then  at  one  jump, 
a  little  more   (change  of  dwelling  in  the  same  place) ;  then  suddenly  and  considerably 

(with  removal  to  another  town)  ;  and  finally  again  more  slowly,  until  there  comes  an 
abrupt  rise  at  the  border  of  a  district  or  country.  (See  K.  Philip,  Finanspolitik  [Copen- 
hagen, 1942],  p.  354.) 

24.  We  may  go  a  step  further  and  assume  that  individuals  are  not  free  to  choose 
a  locality,  but  are  placed  by  the  government  where  they  will  be  most  useful  to  it. 
Then  there  are  no  longer  limits  to  the  interlocal  differences  in  personal  utility.  Instead, 
the  individual  is  so  situated  that  in  no  other  locality  would  his  public  utility  be  greater 
by  more  than  the  traveling  expenses. 

25.  For  this  reason  labor  is  less  mobile  than  goods.  Goods  begin  to  move  when 
price  differences  are  equal  to  the  cost  of  transportation.  Migration,  on  the  contrary, 
does  not  take  place  until  local  differences  in  utility  are  greater  than  travelling  expenses. 
Only  a  modern  gypsy  can  apply  the  same  rule  to  goods  and  to  himself.  But  differences 
in  the  mobility  of  stable  persons,  gypsies,  and  goods  are  evidently  differences  in  degree 
only,  even  where  movement  between  countries  is  concerned.  Whoever  starts  with  the 
assumption  that  labor  is  internationally  immobile  is  dealing  with  a  limiting  case. 

26.  Utility  for  the  individual  can  be  compared  between  localities  at  a  given 
moment,  when  he  really  is  one  and  the  same,  provided  we  interpret  his  choice  of 
locality  as  though  he  had  decided  in  favor  of  the  greater  utility.  But  interpersonal 
utility  comparisons  are  something  entirely  different.  This  would  be  an  interpretation 
of  a  formal  principle  of  explanation  as  an  actual  force,  which  does  not  become  any 
more  real  because  men  believe  in  it  and  calculate  real  wages  and  set  up  wage  schedules 
in  conformity  with  it.    Worship  does  not  transform  an  idol  into  a  god. 


244 


Part  Three.     Trade 


8.    Conclusion 

From  all  that  has  been  said  it  follows,  first,  that  the  objective 
criteria  for  human  choice  of  a  location  vanish  more  and  more  as 
our  model  approaches  reality  until,  in  the  limiting  case  of  the 
individual,  no  choice  remains.  In  the  end  not  much  remained  of 
the  simple  conformity  to  law  of  the  voluntary  spatial  distribution 
that  we  deduced  at  the  beginning  from  special  assumptions.  It  is 
to  be  suspected  that  the  original  precision  was  achieved  by  impos- 
sible assumptions.  This  shows  the  great  psychological  difference 
that  exists  when  we  pass  from  the  general  to  the  particular  instead 
of  from  the  particular  to  the  general,  as  we  have  done  here.  When 
we  proceed  from  the  general  to  the  particular  even  the  special  case 
has  significance  against  the  background  of  the  general,  in  that  it 
gives  a  more  exact  solution  for  certain  conditions.  When  we  start 
with  the  special  case  it  is  soon  covered  over  by  the  more  general 
solution,  and  then  appears  merely  as  an  error  on  the  road  to  truth. 

Secondly,  as  universally  valid  spatial  differences  in  utility  do  not 
exist  in  a  free  economy,  there  is  also  no  limit  for  spatial  differences 
in  nominal  or  real  efficiency  wages.  All  wages  remain  unique  and 
incommensurable  in  space,  and  thus  offer  no  criterion  for  the  spatial 
distribution  of  persons.  Only  where  interlocal  wage  differences  are 
felt  similarly  by  a  sufficiently  large  number  of  persons  can  one-way 
migration  result,  which  in  turn  may,  under  certain  circumstances, 
lead  to  uniform  wage  differentials.     (See  below,  Fig.  91.) 

Only  one  general  principle  can  be  established  for  the  choice  of 
a  location  by  the  individual.  He  will  select  it  so  that  nowhere  else 
does  he  feel  enough  better  to  make  up  for  the  cost  of  moving  and, 
if  necessary,  the  loss  of  familiar  surroundings. 

§2.     The    Location    of   an    Entrepreneur 

An  entrepreneur,  too,  wishes  to  maximize  not  his  profit  in  terms 
of  money  but  his  utility.  For  this  reason  his  profits,  like  the  wages 
of  the  worker,  vary  irregularly  from  place  to  place.  But  as  there 
is  no  "  iron  "  law  of  wages,  though  there  is  a  tendency  toward  an 
"  iron  "  law  of  profits,"^  and  since,  therefore,  entrepreneurial  incomes 
are  especially  sensitive  to  location;  -^  and,  furthermore,  as  an  entre- 

27.  In  other  words,  wages  may  lie  arbitrarily  above  the  minimum  of  existence,  but 
an  entrepreneur's  profit  cannot  exceed  the  enterpreneurial  income  by  an  arbitrary 
amount  without  bringing  counteracting  forces  into  play. 

28.  That  is,  through  the  wrong  choice  of  a  location  it  can  fall  below  the  minimum 


The  Six  Probleius  Disnisscd  I ndh'i dually  245 

preneur,  unlike  a  worker,  is  generally  tied  more  closely  to  his  branch 
of  industry  and,  naturally,  even  more  closely  to  his  own  factory, 
the  choice  of  a  location  by  the  individual  entrepreneur  is  more 
restricted  and  that  of  entrepreneurs  as  a  group  more  calculable 
than  is  the  case  with  luorkers.  Only  when  conditions  in  an  industry 
or  the  capability  of  an  entrepreneur  allow  relatively  large  monetary 
gains,  or  when  the  location  of  entrepreneur  and  enterprise  or  factory 
can  be  separate  without  disadvantage,  is  there  wider  scope  for  free 
personal  choice  of  a  locality. 

Finally,  as  for  the  connection  of  a  choice  of  locality  by  persons 
and  by  enterprises,  it  is  easier  for  an  adequate  number  of  potential 
workers  than  for  potential  entrepreneurs  to  make  the  sacrifice  that 
would  permit  the  establishment  of  a  factory  in  the  locality  of  their 
choice.  (See,  for  example,  the  southward  migration  of  the  American 
textile  industry.)  On  the  other  hand,  migration  from  country  to 
town  offers  examples  enough  of  men  following  factories  either  vol- 
untarily or  of  necessity,  so  that  generalization  in  respect  to  one 
practice  or  the  other  is  impossible.  On  principle,  the  location  of 
men  and  factories  are  interdependent. 

d.  THE  OCCUPANTS  OF  A  LOCALITY 

Who  occupies  any  given  locality?  The  answer  depends,  first, 
upon  what  is  meant  by  "  locality."  The  word  may  have  a  vague 
or  a  precise  meaning.  It  may  be  understood  as  a  group  of  locations  ^^ 
whose  number  can  be  increased,  like  New  York,  or  one  single  spot  ^° 
like  Macy's. 


of  existence  more  easily  tiian  can  the  income  of  a  worker,  especially  as  an  entrepre- 
neur's mistake  cannot  be  so  easily  remedied,  since  the  migration  of  factories  is  incom- 
parably more  expensive  than  that  of  persons. 

29.  In  a  double  sense:  [a)  an  agglomeration  of  areas  through  artificial  increases  in 
a  vertical  direction  (multistory  buildings)  ,  {b)  a  horizontal  agglomeration  of  areas 
that  are  not  employed  for  agricultural  purposes. 

30.  Of  course  even  this  is  still  not  wholly  precise.  The  extremely  difficult  problem 
of  size  of  the  individual  lot  remains,  which  recalls  the  problem  of  "  product  differ- 
entiation," and  the  difficulty  of  determining  precisely  what  a  "  product  "  is.  One  might 
think  of  using  a  legal  criterion,  such  as  the  unit  of  possession.  This  would  be  correct 
if  the  question  were  in  what  way  the  possession  of  a  given  piece  of  ground  could  be 
made  to  yield  the  greatest  possible  total  return.  But  a  discussion  of  basic  principles 
must  not  employ  such  an  institutional  pons  asinorum.  Or  one  might  assume  infinitely 
small  plots  of  ground  together  with  a  prohibition  of  sabotage;  that  is,  no  one  would 
be  allowed  to  withhold  his  land  as  the  "  key  piece,"  but  would  have  to  surrender  it  to 
the  highest  bidder.  In  this  case,  however,  the  question  of  the  production  or  occupants 
of  such  an  infinitely  small  plot  would  have  no  sense,  since  it  would  be  useful  only  in 
combination  with  adjoining  plots.    But  not  only  can   a  given   area  be   combined   in 


246  Part  Three.     Trade 

According  to  circumstances  the  inhabitants  of  a  locality  have 
to  be  compared  among  themselves,  or  with  strangers;  in  the  former 
case  the  comparison  is  directed  toward  similarities,  in  the  latter 
toward  differences.  "  People,"  on  the  other  hand,  might  be  divided 
into  pure  consumers,  persons  with  a  fixed  income,  whose  only 
problem  is  to  spend  it  in  the  most  favorable  locality;  the  others, 
the  producers,  on  the  contrary,  have  this  one  thing  in  common, 
that  their  incomes,  too,  depend  upon  their  choice  of  location.  For 
the  pure  consumer,  therefore,  the  problem  amounts  to  finding  the 
best  residence;  for  the  producer,  to  finding  the  best  combination 
of  business  place  and  residence. 

§1.     Localities    in   the   Wider   Sense 

For  the  most  usual  case,  in  which  residence  and  place  of  business 
coincide,  the  solution  is  this:  There  are  gathered  together  in  one 
locality  all  those  ^^  who  achieve  their  highest  utility  there,  even 
when  loss  of  a  home  and  traveling  expenses  are  subtracted  if 
necessary.^-   This  holds  not  only  for  settlements  but  also  for  larger 


endless  ways  with  other  areas  for  the  same  purpose;  different  men  and  different  prod- 
ucts do  not  always  compete  for  exactly  the  same  combination  or  areas.  This  means 
that  the  assumption  that  the  prices  of  all  remaining  lots  remain  constant  becomes 
impossible,  and  we  can  say  nothing  more  about  the  occupants  or  the  production  of 
one  locality  alone,  but  can  only  determine  the  distribution  of  persons  in  general.  Thus 
our  subject  cannot  even  be  discussed  unless  all  rivals  compete  for  the  same  combination 
of  areas,  however  this  combination  may  be  determined.  Such  a  combination  we  call  a 
locality  in  its  more  restricted  sense. 

31.  Their  number  in  turn  affects  the  utility  of  the  individual  (e.  g.,  through  the 
level  of  rents  and  wages)  . 

32.  The  explanation  for  a  certain  collection  of  people  in  a  particular  place  cannot 
be  found  in  special  common  characteristics  of  its  inhabitants,  any  more  than  special 
characteristics  are  an  explanation  of  why  a  given  group  of  people  belong  to  a  particular 
occupation  or  a  particular  firm.  Such  characteristics  might  become  prominent  either 
through  a  process  of  selection  or  through  mutation.  Furthermore,  any  given  charac- 
teristics are  not  found  in  a  particular  location  only,  nor  are  they  the  only  ones  found 
there.  The  really  revelant  cpiestion  is:  why  are  special  characteristics  used  at  all,  and 
why  are  they  used  in  just  that  particular  place?  With  these  limitations  the  most  recent 
inquiries  into  the  metropolitan  type  of  person  are  really  valuable.  (W.  Hellpach, 
Mensch  und  Volk  der  Grosstadt  [Stuttgart,  1939];  E.  von  Eickstedt,  ed.  Bevolkerrungs- 
biologie  der  Grossstadt  [Stuttgart,  1941];  W.  Mitze,  Die  strukturtypologische  Gliederung 
einer  westdeutschen  Grosstadt  [Leipzig,  1941];  K.  V.  Miiller,  "  Siebungsvorgange  bei  der 
Bildung  von  Grosstadtbevolkerungen,"  Archiv  fur  Bevolkerungswissenschaft,  1942,  pp. 
1-26.) 

All  studies  agree  that  an  especially  large  number  of  gifted  persons  migrate  to  cities; 
similarly,  those  who  move  into  cities  are  predominantly  gifted.  But  on  the  other  hand, 
even  less  well-rounded  personalities  succeed  better  in  urban  specialization. 


The  Six  Piobkins  Discussed  Individually  247 

areas  such  as  economic  landscapes,  countries,  and  continents.  Since 
under  rational  conditions  all  those  assemble  who  find  their  highest 
utility  here  it  follows  that  there  is  good  reason  for  the  special  atti- 
tude toward  space  that  binds  these  persons  together,  such  as  love 
for  a  native  place,  a  feeling  for  economic  landscapes,  and  national 
pride.  Only  when  an  unreasonably  large  fraction  of  the  total 
utility  is  attributed  to  one  of  these  geographical  divisions  may  the 
exaggeration  be  condemned  as  the  outcome  of  local  patriotism, 
particularism,  or  chauvinism. 

§2.     Localities   in   the   Narrower   Sense 

Who  gets  a  location  in  the  narrower  sense,  a  site?  He  who  is 
prepared  to  pay  most  for  it.  This  has  two  implications:  First,  with 
prevailing  price  relations  the  individual  in  question  finds  his  highest 
utility  here.  Secondly,  at  the  price  paid  for  this  site  he  alone  finds 
his  highest  utility  here.  Thus  ground  rent  is  a  price  ^^  whose  func- 
tion is  to  exclude  all  but  one  from  this  locality. 

For  entrepreneurs  the  mechanism  may  be  imagined  as  follows: 
costs,  excluding  the  price  of  the  lot,  are  given  for  each;  so  are  the 
revenues  of  all  locations,  as  well  as  the  prices  of  all  locations  except 
the  one  in  question.  The  locations  can  then  be  arranged  for  each 
entrepreneur  in  order  of  the  total  utility  that  they  will  afford  him. 
If  the  location  to  be  disposed  of  is  to  be  at  the  upper  end  of  the 
series,  that  is,  if  it  is  to  assure  at  least  the  same  utility  as  the  next 
best,  its  price  must  not  exceed  a  definite  calculable  amount.^*  The 
price  may  even  have  to  become  a  subsidy,  especially  if  the  revenues 
to  be  obtained  from  this  location  do  not  even  cover  the  remaining 
costs.  The  various  entrepreneurs  may  now  be  arranged  in  order  of 
the  highest  price  that  they  are  ready  to  pay  for  the  location  in  ques- 
tion.  The  one  at  the  upper  end  gets  it. 

When  we  try  to  compare  the  highest  bidder  with  the  others,  just 
as  when  we  attempted  to  compare  the  personnel  of  an  occupation 
with  others,  we  find  no  further  characteristics  that  would  serve  to 
distinguish  him.  For  example,  he  need  not  be  the  one  who  achieves 
the  highest  gross  profit  here   (proceeds  before  deduction  of  the  cost 

33.  Wherever  rent  appears  as  a  fixed  "  differential  "  ihe  willingness  to  pay  the  price 
is  limited  merely  by  certain  objective  factors  such  as  differences  in  freight  or  in  natural 
yield;  thus,  the  theories  of  site  rent  and  of  rent  based  on  differential  soil  fertility  show 
differences  in  the  prices  of  lots  only  for  certain  simple  cases. 

34.  That  is,  the  amount  that  anyone  is  willing  to  pay  for  a  certain  place  depends 
upon  the  price  at  which  another  site  will  afford  him  a  greater  total  utility. 


2^8  Part  Three.     Trade 

of  the  lot) .  Despite  a  smaller  gross  profit  fie  may  obtain  a  total 
utility  so  high  that  he  outbids  all  the  others. 

When  we  attempt  to  compare,  for  the  highest  bidder,  the  chosen 
location  with  the  competing  localities,  no  criterion  at  all  appears 
save  highest  utility.  The  locality  selected  need  not  offer  him  the 
highest  gross  profit  (before  subtracting  the  cost  of  the  lot)  ;  this 
may  be  greater  elsewhere,  yet  provide  a  smaller  net  profit  because 
of  a  disproportionately  greater  outlay  for  space.  Yet  even  the  net 
profit  may  be  higher  somewhere  else,  for  it  does  not  by  itself  deter- 
mine total  utility. 

In  our  model  of  economic  regions,  in  which  we  restricted  our- 
selves to  monetary  calculations  and  assumed  that  the  competition 
was  sufficient  to  exclude  money  profits,  the  mechanism  is  in  principle 
the  same.  The  price  of  a  site  will  rise  until  all  but  one  would 
produce  there  at  a  loss.^^  The  rising  price  of  land  shifts  the  cost 
curves  upward,  which  reduces  profits  just  as  much  as  when  the 
demand  curve  is  shifted  toward  the  left  by  reduction  in  the  size  of 
a  territory.  The  one  that  remains  is  generally  a  farmer,  since  except 
for  a  few  central  points  industry  would  operate  everywhere  at  a 
loss,  and  so  would  be  able  to  pay  only  a  negative  price  for  land. 
In  our  theoretical  deduction  the  problem  of  the  price  of  land  did 
not  appear,  because  we  neglected  industry's  need  of  space,  arguing 
as  though  industrial  production  could  be  concentrated  at  a  point. 
But  as  factories  are  included  among  the  objects  that  jostle  one 
another  in  space,  local  variations  in  the  price  of  land  cannot  be 
overlooked.  They  are  included  among  the  factors  that  distort  our 
regular  hexagon. 

e.     THE    INDUSTRY    IN    A    LOCALITY 
§1.     Localities   in   the   Wider   Sense 

a.    The  Correct  Solution 

The  firms  in  a  locality  have  this  one  thing  in  common:  their 
entrepreneurs  find  their  highest  utility  there.  But  as  the  influence 
of  an  entrepreneur  on  the  choice  of  a  locality  for  an  enterprise  is 
limited,  especially  when  profits  disappear  under  pure  competition, 
and  as  with  many  corporations  locations  are  determined  exclusively 
by  profitability  rather  than  by  any  sort  of  personal  utility,  a  some- 

35.  This  does  not  hold  with  the  utiHty  calculus.  But  then  money  profits  can  no 
longer  be  excluded,  for  the  returns  to  the  entrepreneur  need  no  longer  he  equal.  The 
case  then  amounts  to  a  normal  one. 


The  Six  Problems  Discussed  Individually  249 

what  narrower  formulation  will  bring  out  the  essential  point  more 
clearly:  In  any  given  locality  everything  is  produced  for  which 
neighboring  competition  leaves  room.^^  It  is  the  difficult  task  of 
those  authorities  who  must  plan  and  develop  cities  or  countries  to 
decide  which  particular  industries  should  locate  in  a  particular  place. 
The  practical  procedure  may  be  imagined  about  as  follows:  First, 
the  chief  production  advantages  of  the  locality  in  question,  and  next 
the  main  cost  factors  for  the  various  enterprises  are  determined, 
from  which  appear  the  industries  for  which  the  local  cost  advan- 
tages will  be  most  advantageous.    So  much  for  supply. 

As  for  demand,  it  would  have  to  be  determined  which  were  the 
industries  whose  nearest  competition  was  unusually  far  distant,  and 
whether  the  intermediate  demand  would  be  adequate.  If  both 
favorable  production  conditions  and  a  satisfactory  distance  from 
competition  exist,  an  undertaking  of  the  type  considered  would 
have  a  good  chance.  Cases  are  much  harder  to  find  in  which  neither 
favorable  conditions  for  production  nor  a  particularly  favorable 
competitive  position  are  manifest,  yet  where  an  enterprise  might 
nevertheless  succeed  in  the  end  against  neighboring  competition.^^ 
The  most  difficult  thing  of  all  is  to  discover  how  the  industries  that 
are  to  be  attracted  will  themselves  reciprocally  alter  the  bases  of 
calculation;  particularly  at  what  price  level  the  final  equilibrium 
will  be  reached. 

Whether  neighboring  production  sites  will  leave  room  for  a  new 
factory  depends  upon  more  than  competition  from  similar  firms. 
As  a  rule  the  product  of  one  locality  differs  in  quality  as  well  as 
packaging  and  the  like  from  similar  products  of  other  localities. 
On  the  whole  it  is  a  somewhat  different  and  characteristic  article 
obtainable  only  there,  and  the  real  question  is  whether  it  can  hold 
its  own  against  all  other  possible  similar  or  entirely  different  goods 
that  consumers  would  otherwise  purchase.  Whether  the  individ- 
uality of  a  locality  can  be  maintained,  whether  the  products  peculiar 
to  it  will  find  an  adequate  market,  whether  it  can  obtain  the  con- 
sumer's goods  peculiar  to  it  at  such  prices  that  a  sufficient  number 
of  people  will  remain  attached  to  it— these  are  the  questions  that 
must  be  answered. 


36.  That  is,  everything  for  which  the  planning  curves  and  demand  curves  at  least 
touch.  The  cost  of  the  particular  site  in  the  locality  must  be  included  in  the  planning 
curve. 

37.  Hence  the  question  is  not  necessarily  one  of  lower  costs  than  in  neighboring 
localities  but  of  sales  adequate  to  cover  them. 


250  Part  Three.     Trade 

p.    The  Traditional  Solution   {The  Principle  of  Comparative  Cost) 

1,      THE     INDUSTRY     OF     A     COUNTRY 

This  classical  location  theory  is  not  wrong,  but  it  is  always 
employed  in  the  wrong  way.  The  theory  tried  to  explain  the  sort 
of  production  that  localities,  economic  landscapes,^^  or  countries  will 
specialize  in.^^  It  could  explain  what  is  produced  by  persons.*"  The 
main  reason  why  the  theory  of  comparative  cost  can  hardly  ever  be 
applied  to  countries  is  their  spatial  extent.  The  theory  of  com- 
parative cost  treats  countries  as  points,  and  believes  it  has  done  all 
that  is  necessary  when  it  has  taken  "  the  "  freight  costs  between 
countries  into  consideration.  But  in  many  cases  these  are  equal  to 
zero,  whereas  up  to  the  frontier  they  almost  never  are.  This  degra- 
dation of  countries  to  points  facilitated  the  erroneous  theory  of 
their  economic  uniformity. 

Such  uniformity  does  not  exist  in  two  respects  that  are  funda- 
mental here:  (1)  Under  the  assumptions  of  the  classical  theory, 
which  was  supposed  to  be  independent  of  political  differences, 
countries  have  no  comparative  advantages  apart  from  those  of  their 
inhabitants  and  localities  (and  of  the  larger  units,  enterprises  and 
econortiic  landscapes  at  most) ;  nor  have  their  inhabitants  and 
localities  any  advantages  in  common  that  would  distinguish  them 
from  the  rest  of  the  world.  For  on  the  one  hand  people  and  the 
gifts  of  nature  vary  from  place  to  place.  These  are  the  differences 
on  the  side  of  supply. 

On  the  other  hand,  demand  varies  in  different  places  and  not 
least  the  demand  from  abroad.*^  Distance  plays  an  important  role 
here.    One  need  only  recall  the  different  situations  relative  to  a 

38.  Depressed  areas  whose  workers  do  not  wish  to  migrate  (see  p.  326,  note  13) 
should  change  over  to  something  wherein  their  greatest  comparative  advantage  lies. 
See  A.  Robinson's  review  of  S.  R.  Dennison's  The  Location  of  Industry  and  the 
Depressed  Areas   (Oxford,  1939)    in  Economic  Journal,  L   (1940)  ,  26. 

39.  The  solution  of  the  problem  is  this:  Every  country  specializes  in  the  goods  that 
it  can  produce  comparatively  more  cheaply. 

40.  Only  in  extreme  cases  can  the  theory  be  applied  more  or  less  to  countries  also; 
perhaps  when  these  are  small,  widely  separated,  and  very  dissimilar  islands,  and  dif- 
ferences in  the  size  and  utilization  of  enterprises  do  not  play  too  important  a  role. 
It  was  probably  not  by  chance  that  the  theory  originated  in  England. 

41.  The  classical  demonstration  proceeds  as  though  the  problem  for  every  country 
in  respect  to  every  product  were  only  to  choose  between  no  market  area  at  all  and  the 
largest  possible  market  area:  the  world.  This  oversimplification  of  possible  market 
areas  is  on  a  par  with  the  oversimplification  of  possible  locations:  choice  is  restricted 
to  a  few  countries.  The  difficulty  of  deciding  on  a  location  in  an  infinite  continuum 
is  avoided  by  dividing  it  into  a  finite  number  of  discontinua. 


The  Six  Problems  Discussed  Individually  251 

foreign  country  of  a  site  located  at  the  frontier  and  of  one  in  the 
interior  of  a  country.  This  location  relative  to  one  frontier  influ- 
ences decisively  the  chances  of  export,  even  when  trade  between 
two  countries  has  to  pass  through  practically  but  one  gateway  in 
each:  Antwerp  to  New  York,  say.  Even  then  the  freight  costs  to 
the  domestic  harbor,  which  are  added  to  the  ocean  freight,  are  often 
higher,  and  always  as  different  as  can  be  for  individual  points  of 
origin  and  destination.  Because  of  these  local  variations  in  supply 
and  demand  absolute  prices  and  comparative  advantages  differ 
everywhere. 

(2)  It  was  explained  in  the  preceding  section  why  absolute 
prices  for  the  same  goods,  and  price  ratios  for  different  goods  within 
the  same  country,  vary  from  place  to  place.  It  must  now  be  added 
that  the  movement  as  well  as  the  level  of  prices  varies  in  different 
localities.  In  other  words,  there  are  no  uniform  national  price 
levels  that  change  abruptly  at  the  frontier.  On  the  contrary,  inter- 
national migration  and  international  trade  connect  domestic  and 
foreign  prices,  especially  near  a  frontier.  A  fundamental  though 
tacit  assumption  of  the  application  of  the  theory  of  comparative 
cost  to  countries  is  not  given  in  reality.*^  The  transitory  possibility 
of  an  independent  central  bank  policy  cannot  alter  this  in  the 
long  run.*^ 

But  this  means  that  countries  simply  do  not  show  the  economic 
uniformity  postulated  by  the  principle  of  comparative  cost;  hence 
it  is  illogical  to  apply  the  theorem  to  them.^*-*''  The  problem  of 
determining  the  production  of  a  country  must  be  solved  in  some 
other  way. 

42.  This  subject  is  treated  at  greater  length  in  my  article,  "  Wo  gilt  das  Theorem 
der  komparativen  Kosten?  "  Weltwirtschaftliches  Archiv,  July,  1938,  pp.  48  f. 

43.  The  long-run  processes  are  unjustly  neglected  today.  Only  they  obey  laws  that 
together  constitute  a  functioning  and  meaningful  whole.  Studies  of  short-run  processes 
are  useful  within  their  limits,  but  are  so  overvalued  at  present  that  the  situation 
borders  on  decadence  and  dissolution.  Keynes,  of  course,  brilliant  as  always,  has 
broken  a  lance  in  their  defense:  In  the  long  run  we  shall  all  be  dead.  But  that  is  just 
brilliant  bluff.  In  the  first  place,  it  is  not  true  of  peoples  as  a  whole;  and  secondly, 
it  often  does  not  hold  for  individuals  either,  since  in  general  a  long  period  means  not 
more  than  a  few  years. 

44.  There  are  still  other  objections.  For  example,  it  is  practically  and  theoretically 
impossible  to  estimate  the  cost  of  an  article  that  is  not  produced  in  a  country  at  all, 
yet  the  principle  assumes  that  it  is  known.  See  Losch,  "  Wo  gilt  das  Theorem  der 
komparativen  Kosten?"  Weltwirtschaftliches  Archiv,  July,  1938,  p.  51. 

45.  Except  for  certain  practical  purposes,  such  as  disproving  the  popular  prejudice 
that  countries  poorly  endowed  by  nature  have  a  more  difficult  time  in  international 
trade.   Since  this  prejudice  regards  countries,  though  incorrectly,  as  units  the  principle 


2r2  ^<J^'   Three.     Trade 

2.       THE     EXPORT    INDUSTRIES     OF     A     COUNTRY 

It  was  characteristic  of  the  theory  of  comparative  cost  that  it 
could  answer  simultaneously  the  two  questions  of  the  industry  of  a 
country  and  of  its  export  industries.  For  since  it  regarded  countries 
as  points  everything  that  they  produced  would  naturally  be  exported. 
But  for  us  the  answers  to  these  two  questions  are  distinct.  Knowing 
what  industries  will  be  profitable  in  a  country  tells  us  very  little 
about  what  that  country  will  export  or  import.  Only  when  we  can 
find  a  new  answer  to  this  question  will  the  theory  of  comparative 
cost  have  been  entirely  replaced. 

Under  the  assumptions  of  the  theory  of  comparative  cost,  which 
were  more  or  less  fulfilled  at  the  time  it  was  developed,  countries 
from  an  economic  standpoint  are  completely  arbitrary  constructs 
to  be  used  as  a  frame  of  reference.  Thus  nothing  remains  but  to 
determine,  first,  the  production  of  all  locations  without  regard  to 
political  frontiers,  then  to  draw  in  these  frontiers  and  consider  their 
effects  upon  the  size  of  the  market  areas.  Then  all  goods  whose 
market  areas  are  intersected  by  frontiers  are  export  goods  if  the 
production  center  lies  within  the  frontier,  and  import  goods  if  it 
lies  beyond.  The  same  is  true  of  supply  areas.*^  This  is  the  solution 
of  the  second  problem  that  the  theory  of  comparative  cost  has  set 
itself. '^^ 


is  perfectly  suitable  for  its  refutation.  And  so  long  as  no  theory  existed  that  could  take 
account  of  the  inherent  multiformity  of  differences  within  a  country,  the  principle 
of  comparative  cost  had  its  place  even  in  the  theory  of  international  trade. 

46.  At  best  the  theorem  might  still  be  applied  to  locations  in  the  narrower  sense. 
Here  net  profit  per  unit  of  land  would  have  the  same  function  as  the  wage  per  unit 
of  time  has  in  the  case  of  persons.  Nevertheless,  this  way  of  looking  at  the  matter  is 
unnecessarily  complicated. 

47.  The  smaller  the  country,  the  larger  the  proportion  of  all  domestic  market  areas 
that  will  be  cut  by  the  border.  Consequently  the  relative  importance  of  international 
trade  diminishes  with  the  increasing  size  of  a  country.  For  example  see  J.  H.  Herberts, 
"  Importance  du  commerce  exterieur  dans  I'economie  frangaise,"  in  L'Activite  £co- 
nomique   (Paris,  1937)  ,  p.  6. 

48.  According  to  B.  Ohlin  {Interregional  and  International  Trade  [Cambridge,  1933]) 
a  country  specializes  in  goods  requiring  factors  of  production  with  which  it  is  rela- 
tively best  endowed.  This  may  or  may  not  be  true.  (See  p.  30,  note  33,  and  pp. 
248  f.)  .  That  local  variations  in  the  scarcity  of  factors  of  production  is  not  a  necessary 
or  even  sufficient  condition  for  the  exchange  of  goods  can  be  seen,  on  the  one  hand, 
from  our  model  of  economic  areas  in  which  trade  is  carried  on  despite  an  equal  dis- 
tribution of  productive  resources;  on  the  other  hand,  there  will  be  no  trade  between 
two  islands  differing  in  nature  and  separated  widely  enough,  despite  all  price  dif- 
ferences. Ohlin  overemphasizes  supply,  as  though  demand  were  less  important.  Yet  he 
would  then  have  to  consider  also  the  prices  of  raw  materials  and  supplies  for  he  does 
not  think  basically  in  terms  of  space. 


The  Six  Problems  Discussed  Individually  253 

Consider  for  a  moment  the  regional  network  for  one  single 
product.  When  individual  markets  are  small  but  countries  large 
it  is  clear  that  some  of  the  regional  centers  will  lie  within  and 
others  beyond  the  border.  In  other  words,  the  same  article  will  be 
both  imported  and  exported,  though  in  different  parts  of  the  same 
country.  On  the  other  hand,  if  the  market  areas  are  large  in  com- 
parison with  countries  and  if  their  centers  are  perhaps  even  con- 
centrated in  a  narrow  space,  as  is  true  of  many  natural  resources, 
certain  countries  will  be  typical  exporters  and  others  typical  im- 
porters of  the  product  concerned. 


§2.     Localities    in   the   Narrower   Sense 

The  solution  of  the  problem  of  the  personnel  of  a  locality, 
mutatis  mutandis,  applies  here  also.  A  locality  in  the  narrower  sense 
goes  to  the  enterprise  that  is  willing  to  pay  most  for  it.  This  can  be 
visualized  by  assuming  that  all  settlements  and  their  industries  are 
given,  with  the  exception  of  one.  Somewhere  in  the  network  of 
settlements,  therefore,  a  gap  is  to  be  filled,  and  the  question  is,  what 
industries  can  squeeze  in  here  and,  inseparable  from  this  question, 
precisely  where  shall  they  be  situated. ^^'^^ 

First,  each  possible  place  is  systematically  examined  to  see  what 
industries  would  be  profitable  if  land  were  free.^^  The  net  profit 
that  it  will  yield  under  this  assumption  shows  the  highest  rent  that 
the  indsutries  in  question  will  be  able  to  pay  for  the  place  under 
consideration.  This  amount  will  be  negative  for  most  industries; 
neighboring  competitors  leave  them  no  room  at  all.  The  few  indus- 
tries that  yield  a  positive  return  will  generally  show  a  profit  at  sites 
that  lie  close  together  at  the  center  of  the  free  space,  or  even  overlap. 
Industries  compete  for  these  favored  sites,  and  not  all  that  could 
exist  with  free  land  will  continue  to  be  profitable  when  competitive 
bidding  begins  to  increase  land  prices  and  to  raise  costs.  Thus  the 
number  of  industries  exceeds  the  number  of  available  sites  at  first, 

49.  It  cannot  be  emphasized  strongly  enough  that  the  frequent  separation  of  choice 
of  region,  choice  of  locality,  and  choice  of  site  is  not  tenable  in  a  strict  sense,  however 
useful  it  may  be  pedagogically.  For  of  what  use  is  a  favorable  locality  if  it  offers  no 
good  sites?   The  problem  of  location  must  be  solved  at  one  stroke. 

50.  We  thus  go  outside  the  most  rigid  formulation  of  the  problem,  since  we  do  not 
assume  the  prices  of  all  lots  except  one  as  given  (in  conformity  with  the  procedure 
in  section  d,  §2,  but  only  the  prices  of  all  except  a  few.  This  broader  formulation  makes 
the  processes  still  clearer. 

51.  In  practice  one  will  have  to  be  content  with  rough  calculations  for  several  likely 
locations.    An  exact  scientific  solution  for  a  concrete  case  is  generally  impossible. 


254 


Part  Three.     Trade 


for  with  free  land  many  enter  the  race  that  come  to  grief  with  an 
increase  in  the  price  of  land.  Prices  are  raised  in  such  a  way  that 
finally  but  one  buyer  remains  for  each  site.  Even  with  relatively  few 
sites  and  competitors  the  determination  of  this  equilibrium  price 
presents  a  difficult  mathematical  problem  (calculus  of  variations) . 
No  simple  solution  exists  for  the  problem  of  who  shall  acquire 
individual  sites  and  at  what  price,  and  who  shall  be  completely 
eliminated. 

This  is  true  even  thougrh  we  have  not  even  considered  the  fact 
that  revenues,  in  turn,  also  depend  on  the  final  result,  especially  on 
the  related  ultimate  determination  of  the  prices  of  the  factors  of 
production,  on  the  exact  location  of  the  railroad  station,  of  the 
road  system,  and  so  on.  The  revenues  at  various  locations  are  as 
much  a  function  of  the  lines  of  communication  as  the  reverse. 
Finally,  there  remains  the  difficulty  that  different  industries  never 
compete  for  exactly  the  same  sites,  but  for  overlapping  ones.  This 
shows  the  great  complexity  of  the  problem.  There  is  no  simple 
method  of  determining  the  industry  that  will  finally  settle  in  a 
locality.  All  that  can  be  given  in  a  few  words  are  the  conditions 
that  the  victorious  enterprise  must  satisfy:  It  must  not  only  be  more 
profitable  at  the  particular  site  than  anywhere  else;  it  must  also 
offer  more  for  this  site  than  the  other  competitors.^^ 

Tables  13  and  14  give  a  very  simple  example  of  the  method  for 
determining  who  is  to  acquire  a  piece  of  ground  and  at  what  price. 
They  show  competition  by  three  industries,  a,  b,  and  c,  for  two  sites, 
I  and  II.  The  winners  are  industry  a,  which  acquires  site  II  at  a 
price  of  4,  and  b,  which  gets  I  at  a  price  of  2.  Industry  c,  on  the 
contrary,  loses  out  even  though  it  shows  relatively  high  gross  receipts. 
It  is  interesting  that  site  I  should  go  to  industry  b  even  though 
industry  a  would  be  still  more  profitable  at  the  purchase  price. 
Table  13  shows  that  at  price  2  for  site  I  industry  a  achieves  a  net 
profit  of  2  on  it,  whereas  industry  b  achieves  a  net  profit  of  only  1. 
Nevertheless  industry  b  alone  fulfills  the  condition  that  not  only 
is  it  more  profitable  at  the  site  obtained  than  anywhere  else,  but 
also  that  it  is  the  highest  bidder,  since  industry  a  prefers  site  II. 


52.  Thus  within  certain  price  limits  there  is  a  bilateral  monopoly.  See  R.  Triffin, 
Monopolistic  Competition  and  General  Equilibrium  Theory  (Cambridge,  Mass.,  1940)  , 
p.  172. 


The  Six  Problems  Discussed  Individually 


Tables    13  and   14.    EXAMPLE   OF  DETERMINATION   OF   THE 
PRICE   OF   LAND 

Competition  among  three  enterprises,  a,  b,  and  c,  for  sites  I  and  II 


Price 
of 

Site 

Net  Profits  of  Enterprise 

Less  Cost  of  Land 

on  Site 

I 

II 

a 

b 

c 

a        !       b 

c 

0 

4 

3 

2 

7 

1 

4 

1 

3 

2 

1 

6 

— 

3 

2 

2 

1 

— 

5 

— 

2 

3 

1 

— 

— 

4 

1 

4 

— 

— 

— 

3 

— 

Table    14 


Price  of  Site 

a 

b 

C 

I 

II 

Chooses  Site 

1 

1 

II 

1 

2 

II 

1 

3 

lor  II 

1 

4 

I  or  II 

I 

2 

1 

I 

II 

2 

2 

II 

2 

3 

T 

II 

2 

4 

— 

3 

1 



II 

3 

2 



II 

3 

3 

• 

II 

3 

4 

■ 

— 

4 

1 

— 

II 

4                    2 

— 

II 

f.     THE    LOCALITY    OF    AN     INDUSTRY" 
§L     Industries   in    General 

a.    The  Regional  Basis 

Industrial  locations  are  usually  not  distributed  at  random,  but 
group  themselves  in  economic  landscapes  with  a  metropolis  as  a 
center  and  a  general  distribution  of  the  remaining  towns  that  is 
favorable  with  respect  to  communication  lines   (see  Chap.  11) . 

p.    Rules  of  Thumb  for  Special  Agglomerations 

Strictly  speaking  all  locations  are  interdependent.  No  one 
location  or  location  factor  can  be  called  leading  and  the  others 
dependent.    The  location  system,  like  the  solar  system,  hangs  free 

53.  Summary  of  the  most  general  conchisions  of  Part  I. 


256  Part  Three.     Trade 

in  space,  so  to  speak,  nowhere  suspended  and  held  together  only 
within  itself.  In  practice,  however,  those  natural  factors  to  whose 
sources  production  is  necessarily  bound  have  special  weight  as  a 
rule:  arable  land,  natural  resources,  valleys,  harbors,  and  climate. 
The  most  important  of  these  are  the  factors  whose  occurrence  is  on 
the  one  hand  limited  and  concentrated  and  to  which,  on  the  other, 
a  relatively  large  amount  of  economic  activity  is  tied.  Natural 
resources,  for  example,  rank  above  soil.  There  still  remains  the 
choice  among  several  possible  sites  of  these  resources,  but  in  many 
cases  the  proximity  and  superior  quality  of  several  natural  factors 
is  so  strikingly  combined  that  such  regions  may  be  regarded  with 
high  probability  from  the  first  as  cardinal  points  in  the  location 
system. 

Other  production  centers,  whose  locations  are  not  uncondi- 
tionally bound  to  natural  resources,  in  the  extreme  case  those  that 
by  nature  are  strongly  consumer  oriented,  are  more  or  less  attracted 
to  this  leading  concentration  or  at  least  located  with  respect  to  it. 
The  resulting  aggregation  of  populations  finally  results  in  large- 
scale  enterprises  such  as  would  have  been  impossible  with  more 
equal  distribution.  The  extent,  importance,  and  proximity  of  these 
favored  localities  determine  whether  only  regional  centers  will  arise 
in  them,  or  whole  regional  systems  more  concentrated  than  else- 
where, though  often  concentrated  to  the  point  where  they  can  no 
longer  be  recognized.  It  is  mainly  the  need  of  space  for  agriculture 
that  prevents  complete  concentration  of  industrial  production  and 
of  trade  in  a  few  places.  For  this  reason  even  the  urban  population 
is  much  more  uniformly  distributed  in  predominantly  agrarian 
countries.  As  soon  as  the  important  group  of  agricultural  consumers 
is  widely  distributed  the  advantages  and  disadvantages  of  distance 
begin  to  play  a  role  for  many  industries.  Their  concentration  breaks 
up,  which  in  its  turn  causes  other  branches  of  industry  to  follow 
them.  In  the  language  of  economics:  The  more  the  market  net- 
works expand,  the  greater  becomes  the  distance  between  the  centers 
of  individual  markets. 

We  shall  neglect  historically  determined  inconsistencies,  though 
in  practice  they  are  temporarily  very  important.  The  Chinese 
mineral  deposits,  for  instance,  would  have  led  to  a  much  more 
intense  concentration  of  the  population  if  the  economic  develop- 
ment of  the  country  had  not  been  so  backward.  But  a  respect  for 
history  must  not  be  carried  to  the  point  of  contempt  for  logic. 
Here  we  are  interested  in  the  rules  of  thumb  for  logical  distribu- 
tion, not  for  the  distribution  that  has  actually  occurred.    Examples 


The  Six  Prohlons  Discussed  Individually  257 

will  be  offered  only  if  they  permit  a  logical  as  well  as  a  historical 
explanation. 

The  importance  of  source  is  obvious  in  the  distribution  of  popu- 
lations in  both  Europe  and  the  United  States.^*  Why  is  the 
population  of  the  North  American  continent  concentrated  in  the 
northeastern  part  of  the  United  States?  ^^  The  most  important 
reason  is  the  climate:  too  cold  in  the  North,  too  hot  in  the  South/^ 
too  dry  in  the  West.  Then  the  soil:  on  the  whole  it  is  poorer  in 
the  West  than  in  the  Middle  West  and  the  East,  and  often  below 
the  requirements  for  grass,  not  to  mention  grain. 

Climate,  soil  quality,  and  man  co-operated  to  produce  the  result. 
In  the  South  some  of  the  soil  is  very  good  even  today,  an  example 
of  the  fact  that  a  natural  factor  alone  is  of  no  great  significance. 
Natural  resources  are  not  unequivocally  on  the  side  of  the  North- 
east, though  they  may  give  it  a  slight  advantage. ^^  Its  situation  in 
respect  to  communications,  on  the  contrary,  is  unusually  favorable. 
It  lies  nearest  the  industrial  areas  of  Europe,^^-^^  has  the  best  harbors, 

54.  We  combine  discussions  of  the  distribution  of  people  and  of  their  industries. 

55.  The  boundaries  for  the  rectangle  of  dense  population  are  about  as  follows: 
a  vertical  line  west  of  Iowa;  in  the  east,  the  ocean;  a  horizontal  line  through  Montreal 
to  the  north  and  another  through  Washington  to  the  south  (somewhat  further  south 
for  the  agricultural  population  as  a  whole.  See  Fig.  64) . 

56.  The  hotter  the  climate  the  less  dense  must  be  the  agricultural  population  with 
the  same  soil,  the  same  crops,  and  the  same  plane  of  living,  and  the  larger,  therefore,  the 
individual  farm.  Even  when  the  heat  does  not  affect  natural  fertility  it  prevents  the 
intensive  use  of  the  soil  that  is  possible  further  north,  though  these  differences  must 
not  be  exaggerated.  In  the  United  States,  of  course,  it  is  not  so  much  the  agricultural 
as  the  industrial  population  that  is  concentrated  in  the  Northeast.  This  is  due  partly 
to  historical  reasons.  The  feudal  system  in  the  South  and,  after  its  collapse,  the  after- 
math of  the  Civil  War,  which  manifestly  broke  the  backbone  of  the  South,  did  not 
favor  any  extensive  influx.  But  a  more  important  reason  was  that  most  of  those  who 
did  come  in  were  accustomed  to  a  northerly  climate,  in  which  they  were  more  efficient 
and,  perhaps  most  important  of  all,  in  which  they  felt  better.  In  this  case  the  influence 
of  climate  probably  makes  itself  felt  through  consumption  rather  than  through 
production. 

57.  In  the  South  (ore  and  coal)  and  near  Duluth  (ore;  coal  as  a  cheap  return 
freight)  iron  and  steel  could  be  produced  more  cheaply,  but  their  relation  to  the 
market  is  so  unfavorable  that  factories  cannot  reach  their  optimum  size,  at  least  near 
Duluth.  See  A.  Predohl,  "  Die  ortliche  Verteilung  der  amerikanischen  Eisen-  und 
Stahlindustrie,"  Weltwirtschaftliches  Archiv,  XXVII    (1928),  286  ff.,  329*. 

58.  Which  includes  the  fortuitous  advantage  that  when  immigrants  arrived  from 
Europe  over  the  shortest  route  they  landed  in  the  Northeast  and  at  first  remained 
there. 

59.  Even  though  certain  freights  to  Europe  are  now  the  same  for  all  harbors  on 
the  East  Coast  despite  the  different  distances,  the  time  costs  such  as  interest  can  still 
be  saved  over  the  shorter  northern  route. 


258 


Part  Three.     Trade 


and  the  waterways  of  the  Great  Lakes.  Of  course  artificial  measures- 
like  the  politically  rather  than  economically  determined  dis- 
crimination of  freight  rates  to  the  disadvantage  of  its  great  rival, 
the  Mississippi  Valley— have  strongly  emphasized  the  natural  advan- 
tages of  the  Northeast. 

The  belt  of  strikingly  dense  population  that  stretches  slightly 
southward  from  the  English  industrial  areas  across  northern  France 
and  Belgium,  southern  Holland,  the  Ruhr,  central  Germany,  Saxony, 
Upper  Silesia  and  the  neighboring  parts  of  Bohemia  and  southern 
Poland,  into  northern  Rumania  and  the  Ukraine,  where  it  turns 


Inhabitants  per 
square  kilometer 


Over  100 


60-100 


25-50 


1-25 


Fig.   55.   Population   density   of   northeastern   Europe, 
about  1930.    (After  Goode  and  others.) 

toward  the  northeast  in  the  Donets  area,^°  is  chiefly  attributable  to 
the  presence  of  natural  resources,  particularly  iron  and  coal.  But 
the  fertility  of  the  soil  on  the  northern  edge  of  the  German 
Mittelgebirg  Chain  and  the  Carpathian  Mountains  also  plays  a  part, 
especially  in  the  areas  of  black  soil.^^   So  does  a  naturally  favorable 


60.  It  is  really  astonishing,  and  further  proof  of  the  attraction  of  large  aggregations, 
how  regularly  the  population  density  falls  off  with  distance  from  this  belt,  especially 
toward  the  north.  In  the  south  the  pattern  is  distorted  by,  among  other  things,  a 
second  densely  populated  belt  that  runs  up  the  Rhine  Valley  and  continues  on  the 
other  side  of  the  Alps  down  to  the  tip  of  Italy   (See  Fig.  55)  . 

61.  According  to  Haufe  this  belt  was  very  thickly  settled  even  before  the  days  of 
industrialization  {Die  Bevolkerung  Europas  [Berlin,  1936],  Map  1) .  On  the  relative 
locations  of  industry  and  especially  productive  agriculture  to  one  another,  see  O.  Schlier, 
"  Regionale  Statistik,"  Weltwirtschaftliches  Archiv,  LIV    (1941)  ,  292. 


I 


The  Six  Problems  Discussed  Individually  259 

situation  in  respect  to  communications,  for  example,  with  London, 
the  lower  Rhine,  and  central  Germany. 

Be  it  repeated  that,  strictly  speaking,  this  is  no  explanation  of 
reality,  because  it  omits  not  only  historical  factors  but  also  the  whole 
interdependence  of  economic  forces.  But  as  a  first  approximation, 
and  above  all  in  the  face  of  such  extensive  regional  differences,^^  j^ 
is  useful  to  put  the  most  important  factors  into  the  center  of  the 
picture  even  though  they  are  not  the  sole  effective  ones.  The  idea 
was  not  to  provide  a  complete  derivation  of  a  rational  choice  of 
location.  The  result  is  not  conclusive,  though  it  is  probable.  Such 
limited  rules  of  thumb  are  more  important  in  practice  than  scien- 
tifically exact  emphasis  on  boundless  interdependence. 

§2.     The   Individual   Industry 

a.    In  General 

The  individual  agricultural  and  industrial  enterprises  are  of 
such  size  and  so  distributed  in  space  that  the  total  number  of 
independents,  and  in  this  context  the  income  of  every  individual, 
is  maximized.  Accordingly  a  single  good  is  produced  in  as  many 
localities  as  possible S'^  The  solution  might  be  visualized  in  some 
such  way  as  this.  A  network  of  market  areas  small  enough  to  allow 
no  profits,  at  least  to  a  marginal  entrepreneur,  is  placed  over  a  region. 
It  is  shaped  and  placed  in  such  a  manner  that  the  demand  for  the 
individual  is,  nevertheless,  as  large  as  possible.''*    (See  pp.  94  f.) 

p.    The  Individual  Enterprise 

1.      THE    GENERAL    SOLUTIONIS 

Corporations  erect  a  factory  where  it  will  yield  the  greatest  profit 

62.  The  more  we  get  down  to  single  localities  the  more  important  do  the  other 
factors  become. 

63.  This  is  true  only  for  given  techniques.  Technical  progress  may  bring  out  the 
opposite  tendency— to  decrease  the  number  of  producers. 

64.  The  choice  of  a  locality  by  an  industry  depends  upon  maximization  of  the 
producers,  the  choice  of  an  industry  for  a  locality  upon  maximization  of  the  ground 
rent.  The  first  tendency  determines  the  regional  network  for  a  product  when  the  site 
and  size  of  the  networks  for  all  other  goods  are  given.  The  second  regards  the  networks 
themselves  as  given,  and  determines  their  relation  to  one  another. 

65.  I  have  disproved  elsewhere  the  solution  given  by  the  theory  of  comparative  cost: 
"A  factory  chooses  that  locality  where  the  comparative  advantage  for  its  type  of  pro- 
duction is  greatest."  ("  Wo  gilt  das  Theorem  der  komparativen  Kosten?  "  Weltwirt- 
schaftliches  Archiv,  July,  1938,  pp.  50  f.) 


25<)  Part  Three.     Trade 

(if  market  conditions  show  monopolistic  elements) ,  or  at  least  where 
it  can  just  continue  to  exist  with  a  normal  return  on  the  capital 
invested  (pure  competition) .  Such  a  location  is  objectively  unequi- 
vocal. Individual  entrepreneurs  may  choose  another  location,  since 
they  are  not  concerned  with  money  profit  but  with  the  greatest  total 
utility.  The  scope  for  this  subjective  choice  of  a  location  is  objec- 
tively limited,  since  at  most  it  may  cost  profits  and  the  entrepre- 
neurial wage.***^ 

Monopolistic  profits  are  possible  chiefly  in  five  cases:  (1)  When 
the  amount  offered  is  limited.  (2)  When  the  number  of  producers 
is  limited.  (3)  When  even  with  free  entry  their  number  is  small 
relative  to  the  size  of  the  market,  so  that  new  entrepreneurs  can 
enter  only  discontinuously.  (4)  When  the  market  areas  cannot  be 
reduced  exactly  to  the  smallest  necessary  size  because  of  the  discon- 
tinuity of  the  original  settlements.  (5)  For  those  entrepreneurs 
who  are  more  skillful  than  the  marginal  producer.*'^ 

But  in  all  cases  where  entry  into  an  industry  is  free,  where  the 
number  of  possible  enterprises  is  large,  and  development  goes  on 
smoothly,  the  pressure  of  potential  entrepreneurs  always  tends  to- 
ward the  elimination  of  profits  and  a  condensation  of  locations 
accordingly.  In  this  case  an  enterprise  is  established  simply  where 
it  can  exist.  Its  existence  depends  primarily  also  upon  the  location 
of  neighboring  enterprises  that  compete  either  for  sales  or  for  factors 
of  production.  If  a  new  bank,  say,  is  to  be  founded,  a  gap  in  the 
already  existing  bank  network  must  be  found  that  will  assure  an 
adequate  supply  area  of  deposits  on  the  one  hand,  and  an  adequate 
market  area  for  bank  credits  on  the  other. 

2.       SPECIAL     CASES 

A  few  special  solutions  that  have  dominated  the  past  literature 
are  valid  only  in  the  rare  cases  in  which  their  very  restrictive  assump- 
tions are  fulfilled. 

1.  A  factory  chooses  the  locality  with  lowest  freight  costs.  This 
assumes  that  production  costs  are  the  same  everywhere,  and  also 
that  the  number  and  demand  of  consumption  centers  are  unchange- 
able.   If  their  number  is  variable  the  total  freight  or  the  average 

66.  True  in  a  free  economy.    For  a  planned  economy  the  statement  must  read:  An 
enterprise  will  be  established  where  it  can  best  serve  the  interests  of  the  government. 

67.  In  a  strict  sense  (1)  and  (2)  are  rents  that  depend  upon  natural  or  artificial 
scarcity;    (3)    and    (4)    profits  due  to  indivisibility;  and    (5)    an  entrepreneurial  wage 

(F.  Machlup,  "  Competition,  Pliopoly  and  Profit,"  Economica,  1942,  p.  164) . 


Tlie  Six  Problems  Discussed  Individually  261 

freight  would  be  lowest  when  sales  remained  limited  simply  to  the 
producing  locality.  If  the  number  of  consuming  localities  is  fixed 
but  their  demand  is  variable,  one  of  two  localities  may  still  show 
the  lower  total  and  average  freight;  but  only  because  the  demand 
from  remote  points  is  too  small  to  be  of  any  importance.  A  shifting 
of  the  location  in  their  direction  might  increase  their  demand  so 
much,  and  need  decrease  so  little  the  demand  of  places  that  now 
become  more  distant,  as  to  make  the  new  location  more  favorable 
in  spite  of  its  higher  freight  costs.  Indeed,  the  increased  demand 
might  lower  costs  so  greatly  that  the  price  might  fall  even  in  the 
deserted  location.  Finally,  the  first  condition  for  location  at  the 
point  of  least  freight  cost,  namely  that  production  costs  are  equal 
at  different  locations,  is  seldom  fulfilled  even  in  times  of  uniform 
prices  and  uniform  wages. 

2.  A  factory  chooses  the  locality  with  the  lowest  cost  of  pro- 
duction.^^ Obviously  this  is  true  only  when  shipping  costs  and 
personal  contact  with  the  customer  play  no  role.  In  this  rare  instance 
all  factories  of  the  same  branch  of  industry  collect  in  this  one  locality. 
It  should  be  said  at  the  same  time,  however,  that  local  costs  are  never 
constant  but  depend  in  turn  upon  their  power  of  attraction.  Local- 
ities with  favorable  cost  curves  naturally  exert  a  special  drawing 
power,  but  it  cannot  be  emphasized  strongly  enough  that  much 
depends  also  upon  their  position  with  respect  to  one  another  and 
to  consumers.  The  final  list  of  locations  need  by  no  means  contain 
the  localities  with  lowest  cost  of  production. ^^-^^ 

3.  A  factory  chooses  the  locality  with  lowest  delivered  price 
(production  costs  -f  freight  on  the  finished  product) .  Weber  and 
Palander  have  been  principally  occupied  with  this  case,  of  which 
one-sided  production  or  transportation  orientation  constitute  only 
limiting  cases.    All  the  objections  already  brought  forward  under 

(I)   and   (2)   apply  to  it.    The  assumptions  of  this  solution  are  ful- 
filled only  under  exceptional  circumstances. 

68.  Unlike  the  case  of  pure  production  orientation  discussed  on  p.  23,  these  include 
also  the  freight  on  raw  materials  and  supplies. 

69.  Suppose  a  mine  is  to  work  an  especially  rich  vein.  The  main  problem  of  this 
individual  enterprise  is  as  follows:  Is  there  a  sufficiently  large  uncontested  territory 
(do  supply  and  demand  curves  intersect)  ?  But  for  the  mining  industry  at  large  this 
does  not  yet  settle  the  question.  The  particular  mine  may  be  profitable,  but  perhaps 
the  total  number  of  entreprises  could  be  increased  if  all  mines  were  so  distributed  that 
instead  of  this  single  mine,  two  others,  perhaps  less  rich  and  so  profitable  only  alterna- 
tively with  this  one  could  be  worked. 

70.  In  agriculture,  too,  pure  transportation  or  pure  production  orientation  are 
obviously  marginal  cases  and  interdependence,  on  ihc  contrary,  is  the  rule.  Neither  the 
best  nor  the  nearest  land  need  be  cultivated. 


262  Part  Three.     Trade 

g.     CONCLUSION 

The  division  of  labor  is  determined  by  the  two  great  principles, 
necessity  and  inclination.  By  necessity  when  producers  (person  or 
enterprises)  can  just  barely  exist,  but  in  turn  should  be  as  numerous 
as  possible;  by  inclination  when  a  fixed  number  of  producers  attempt 
to  maximize  their  utility.  In  the  first  case  the  income  of  the  indi- 
vidual is  constant  and  the  number  of  income  recipients  is  variable; 
in  the  second  the  situation  is  reversed.  However,  the  variable  should 
always  be  maximized.  Now  as  a  rule  the  number  of  individual 
producers  (workers)  at  any  one  time  is  fixed,  that  of  producing 
combinations  and  their  leaders  (enterprises  and  entrepreneurs) ,  on 
the  contrary,  always  variable;  that  is,  the  constant  number  of  pro- 
ducers can  be  collected  into  a  smaller  or  larger  number  of  groups. 
If  Malthus  were  right,  if  man,  like  the  lower  animals,  continued 
to  multiply  so  rapidly  that  each  individual  would  be  just  able  to 
exist,^^  there  would  be  no  such  difference.  But  because  man  restrains 
his  multiplication  his  income  rises  above  the  minimum  of  subsis- 
tence (profits  from  work) ,  and  there  is  scope  for  his  inclinations. 
It  is  precisely  the  employed  rather  than  the  independent  producers 
that  are  free  within  these  limits  to  choose  a  location.  In  contrast 
to  these,  the  smaller  number  of  independents  can  be  increased  at 
will  from  the  great  reservoir  of  the  employed.  Their  lot  therefore 
resembles  that  of  enterprises.  Their  choice  of  a  location  is  decided 
more  by  necessity  than  by  inclination,  and  there  is  a  perpetual 
tendency  to  eliminate  again  the  entrepreneurial  profit,  which  would 
allow  some  degree  of  freedom  to  the  entrepreneur  also.  There  is 
more  an  "  iron  law  of  profits  "  than  an  "  iron  law  of  wages."  Any 
entrepreneurial  profits  that  appear  nevertheless,  may  be  attributed 
for  the  most  part  to  the  same  cause  as  the  "  profits  from  work  ";  the 
limited  multiplication  of  man.  Thanks  to  this,  man  can  place  him- 
self largely  as  he  likes  in  the  great  spatial  division  of  labor,  whereas 
enterprises  necessarily  tend  at  least  to  seek  gaps. 


71.  Of  course  the  minimum  of  existence  of  a  nation  lies  above  that  of  its  individual 
citizens,  for  certain  necessary  functions  cannot  be  performed  by  persons  who  are  only 
just  able  to  exist. 


Chapter  18.     Price  Gradients 


In  a  free  economy  the  spatial  division  of  labor  is  guided  by 
geographical  price  differences.  In  equilibrium  these  often  constitute 
regular  gradients  of  three  types:  (1)  The  price  in  any  part  of  a 
single  supply  or  market  area  differs  from  the  central  price  at  most 
by  the  costs  of  distance.  The  resulting  price  cones  and  price  funnels 
make  up  the  market  gradient.  (2)  If  a  commodity  is  produced  at 
the  same  time  on  several  levels  of  an  economic  landscape  hierarchy, 
that  is,  in  localities  of  different  size  and  rank,  a  landscape  gradient 
may  arise  among  central  prices  in  these  localities.  (3)  Price  dif- 
ferences occur  also  between  different  economic  landscapes  in  local- 
ities of  equal  importance:  a  world  gradient,  of  which  national  and 
continental  differentials  represent  sectors. 

Landscape  and  world  gradients  apply  to  goods  of  different  pro- 
ducers; market  gradients  affecting  industrial  products  apply  to  goods 
of  the  same  producer.  All  these  differences  are  at  most  equal  to 
the  costs  of  distance  in  the  broad  sense,  which  also  includes  trade 
margins.  Even  within  the  limits  of  these  differences  all  prices  are 
uniquely  determined;  each  is  such  that  the  conditions  of  locational 
equilibrium  are  fulfilled. 


1.  Here  it  is  possible  only  to  sketch  what  is  discussed  at  length  in  my  Geographic 
der  Preise  (in  preparation)  and  Zur  Beurteilung  des  westostlichen  Preisgejiilles  (unpub- 
lished monograph)  . 

263 


B.   Disturbance  of  the  Equilibrium 

The  theory  of  trade  has  two  tasks;  First,  to  explain  the  principles 
of  the  division  of  labor  and,  second,  to  show  the  mechanism  by 
which  they  prevail  against  disturbances.^  The  first  task  has  already 
been  discussed  in  the  preceding  chapters;  the  second  will  be  taken 
up  in  the  following  one.^ 


1.  I  dismiss  as  insoluble  a  third  traditional  task;  to  calculate  the  gains  from  inter- 
national trade. 

2.  The  most  important  results  are  summarized  in  my  article,  "  Eine  neue  Theorie 
des  internationalen  Handels,"  Weltwirtschaftliches  Archiv,  1939.  But  only  the  detailed 
presentation  offered  here  will  provide  a  complete  understanding. 

264 


Chapter  19.     Self-Regulation 


a.     TRANSFER    OF    PRODUCTS    DURING    SHORT-RUN 
DISTURBANCES     (THE    TRANSFER    PROBLEM)  ^ 

A  change  in  the  division  of  labor  even  between  two  localities 
only,  eventually  alters  the  whole  system  through  movements  of 
prices.  The  effects  of  a  temporary  disturbance  are  substantially 
exhausted  by  shifts  in  income,  fluctuations  in  the  volume  of  employ- 
ment, changes  in  the  place  of  employment  but  only  seldom  in  that 
of  residence,  and  a  rearrangement  in  the  flow  of  goods  and  of  capital. 
In  short,  the  size  and  composition  of  the  balance  of  payments  change, 
but  the  locational  pattern  as  a  whole  is  unaltered.  Everything  con- 
nected with  these  price  fluctuations  (how  they  come  about,  what 
form  they  take,  their  locality,  time,  direction,  extent,  and  effect) 
is  among  the  most  important  topics  of  the  theory  of  international 
trade.  We  shall  discuss  here  these  aspects  of  price  fluctuations  for 
the  most  important  subjects  and  the  spatial  constructs  that  are  used 
as  a  frame  of  reference  in  international  trade. 

§1.     Individuals 

Let  us  start  with  very  simple  conditions.  Suppose  the  demand 
for  the  work  of  the  cobbler  Jung  increases  because  he  has  joined  a 
large  club,  the  members  of  which  now  favor  him.  He  will  ask  a 
slightly  higher  price,  if  not  because  he  is  anxious  for  profits  then 
at  least  because  his  work  has  become  more  irksome  because  of  the 
longer  hours.  On  the  credit  side  of  his  balance  of  payments,  the 
value  of  his  "  export  "  increases;  first,  because  he  commands  a  higher 
price;  second,  because  he  works  longer  hours;  and  third,  because 
he  now  finds  it  advantageous  to  give  up  much  of  the  work  that  he 
used  to  do  about  his  home  and  to  repair  shoes  instead.  The  situation 
corresponds  to  the  diversion  of  production  from  a  domestic  market 
to  exports  in  international  trade.    On  the  debit  side,  the  value  of 

1.  Here  it  is  my  purpose  to  explain  the  new  fundamental  ideas,  whereas  my  theory 
is  presented  more  compactly  but  systematically  more  completely  in  my  article,  "  Die 
Lehre  vom  Transfer— neu  gefasst,"  Jahrbiicher  fiir  Nationaloknonmie,  CLIV  (1941) , 
385-402. 

S65 


o(35  Port  Three.     Trade 

his  "  imports  "  increases.  First,  for  the  reason  just  mentioned  of  a 
simple  shift  in  production.  He  will  no  longer  paint  his  garden  fence, 
for  example,  but  will  have  this  work  done  for  him.  Second,  because 
with  his  larger  income  he  can  afford  more.  Whatever  remains  he 
will  deposit  in  the  bank.  In  other  words,  he  will  expand  his  capital 
export.  The  prices  of  most  of  the  goods  that  he  buys  will  hardly 
increase,  because  on  the  whole  his  customers  or  his  competitors  will 
now  buy  less  of  those  articles  on  which  he  spends  more;  besides,  the 
amounts  are  so  dispersed  as  not  to  affect  prices. 

Of  course  he  may  be  more  free  with  his  money,  less  careful  about 
his  purchases,  shopping  in  more  expensive  stores  and  there  paying 
higher  prices  even  when  they  do  not  correspond  to  better  quality. 
The  landlord  may  have  the  best  chance  to  profit  from  his  increased 
prosperity  by  raising  his  rent.  Our  cobbler  now  lives  in  an  atmos- 
phere of  prosperity:  He  asks  higher  prices,  pays  more  rent,  spends 
more  freely,  and  deposits  more  in  the  bank.  The  opposite  of  all 
this  applies  to  his  competitors,  though  to  a  much  smaller  degree, 
since  their  loss  is  divided  among  many.  The  cobbler  nearest  to 
Jung  will  be  most  severely  affected,  since  even  club  loyalties  weaken 
with  distance. 

One  day  a  new  tax  bill  arrives  unexpectedly  and  puts  to  Jung 
the  same  problem  that  Germany  had  with  reparations:  A  unilateral 
transfer  must  be  made.  His  "  import  of  goods  "  and  his  "  export 
of  capital,"  both  of  which  he  will  decrease  with  a  sigh,  will  most 
likely  bear  the  chief  burden;  he  will  spend  less  and  be  able  to  save 
less.  But  in  addition  pressure  will  be  exerted  upon  the  whole  level 
of  high  prices  that  surrounds  Jung.  Forced  by  necessity,  he  will 
again  buy  more  carefully;  he  will  bargain  with  his  landlord,  and 
reduce  his  prices  somewhat,  in  order  to  recover  at  least  a  part  of 
the  tax.  In  short,  Jung  will  pass  through  a  deflationary  crisis.  This 
crisis  will  be  aggravated  if  other  cobblers  should  now  join  the  club  " 
in  order  to  take  away  the  customers  that  Jung  had  just  gained,  and 
until  the  tax  has  been  paid  he  may  even  be  worse  off  than  ever— 
until  at  last  everything  is  as  it  was  in  the  beginning. 

Thus  does  the  mechanism  that  is  familiar  to  us  only  on  a  large 
scale  operate  in  miniature,  and  with  different  emphasis.  We  shall 
now  examine  it  once  more  and  in  greater  detail  for  larger  economic 
units  than  the  individual. 

2.  If  this  does  not  work,  and  the  loss  of  customers  has  to  be  regarded  as  permanent, 
one  or  another  of  the  cobblers  a  few  blocks  from  Jung  will  move  away  in  order  to 
gain  more  customers.  Here  we  embark  on  the  combination  problem,  to  be  discussed 
later. 


Self-Regulation  267 

§2.     Factories 

Suppose  that  a  Stuttgart  shoe  stored  suddenly  orders  1,000 marks' 
worth  of  shoes,  which  it  formerly  ordered  from  a  local  seller  B,  from 
J5i,  located  in  a  smaller  place  such  as  Tuttlingen.  The  additional 
demand  for  shoes  from  this  town  will  raise  their  price,  partly  because 
the  Tuttlingen  firm  has  to  fear  only  imperfect  competition,  but 
perhaps  also  because  its  production  can  be  expanded  only  at 
increasing  cost.  By  offering  higher  wages,  it  will  attract  additional 
workers  away  from  other  local  enterprises.  If  this  does  not  suffice, 
further  wage  increases  will  enlarge  the  supply  area  of  commuting 
workers  at  the  expense  of  neighboring  factories,  and  wages  will 
finally  rise  so  high  that  labor  will  be  attracted  from  a  distance. 
This  in  turn  will  raise  rents.  The  building  boom  that  results  will 
increase  the  pay  of  masons  and  other  artisans.  Vegetables  and  milk 
will  become  dearer  because  their  supply  area  has  to  be  enlarged; 
in  brief,  the  local  price  level  will  rise.  It  is  of  fundamental  impor- 
tance, and  of  the  very  essence  of  the  theory  presented  in  these  pages, 
to  have  an  exact  idea  of  the  further  course  of  such  a  local  price 
change. 

<x.   Price  Waves  and  How  They  Spread 

We  can  distinguish  a  direct  and  an  indirect  spread  of  a  local 
price  change.  Distant  customers  of  and  sellers  to  the  firms  involved 
will  be  directly  affected;  the  prices  of  competitors  and  those  of  other 
goods  will  be  affected  indirectly.  The  direct  spatial  spread  of  a 
local  price  inflation  (hatched  in  Fig.  56)  is  retarded  by  freight  costs 
and  neighboring  competition.  However,  the  effects  of  the  inflation 
on  the  region  controlled  by  its  point  of  origin  are  twofold.  The 
higher  price  of  its  own  products  narrows  their  market  area  (in  Fig. 
56,  for  instance,  from  radius  B\G\  to  B'lG'z) ,  and  the  higher  prices 
of  imported  goods  widen  their  supply  area  (for  example,  from  B\D\ 
to  B\D'^  ,  always  to  the  advantage  or  disadvantage  of  neighboring 
competitors.  The  increase  in  prices  does  not  operate  uniformly 
throughout  these  market  areas.  Though  for  all  goods  it  is  relatively 
greatest  in  the  "  last  "  production  locality,  this  "  last  "  locality  is 
the  central  point  {B\)  for  the  area  for  export;  and  the  border  {D'2, 
for  instance)  for  the  import  area,  which  happens  to  be  the  location 
where  no  freight  costs  (which  need  not  rise  concomitantly)  are 
included  in  the  price. 

The  indirect  spatial  extension  of  a  local  increase  in  prices  goes 
further.  At  first  it  is  transmitted  to  the  adjoining  competitors  of  B\. 
If  B\  enlarges  its  supply  area  at  the  expense  of  B\  by  raising  prices. 


268 


Part  Three.     Trade 


the  scarcity  of  imports  will  raise  prices  in  B'2  also,  though  not  quite 
so  high  as  in  B\,  since  the  special  cause  operating  there  is  absent. 
B'z,  on  its  part,  now  constitutes  a  new  "  focus  of  infection  "  for 
localities  that  B\  can  no  longer  affect  directly.  In  addition  the  price 
inflation  is  transmitted  to  other  goods,  not  only  through  the  pro- 
ducers selling  to  B\  but  also  indirectly  through  its  customers,  who 
spend  more  money  for  other  things  after  B\  increases  the  price  of 
its  shoes. 


^;      ^i 


Fig.  56.   Effects  of  a  price  inflation  on  market  areas 


(3.    The  Direction  of  Price  Waves 

Price  waves  always  move  away  from  their  point  of  origin.  Each 
consecutive  temporal  and  spatial  link  in  the  chain  of  purchasing- 
power  transfers  is  necessarily  farther  removed  from  the  starting  point 
than  the  preceding  one.  For  a  recipient  of  increased  purchasing 
power  will  turn  it  to  better  account  in  a  direction  away  from  the 
source  (Tuttlingen,  in  our  example) ,  where  prices  have  not  yet 
been  driven  upward.  And  those  factories  affected  by  the  falling-off 
of  purchasing  power  in  Stuttgart  will  endeavor  to  dispose  of  their 


Self-Regulation  269 

goods  in  the  opposite  direction  from  that  city,  because  nearer  Stutt- 
gart they  encounter  the  still  stronger  price-cutting  competition  of  B. 

y.    The  Damping  of  Price  Waves 

As  the  price  change  widens,  its  intensity  diminishes  for  four 
different  reasons. 

1.      DECREASING    INFLUENCE    OF    THE    POINT    OF    ORIGIN 

Not  only  are  the  supply  and  market  areas  of  a  locality  B  definitely 
restricted  by  freight  costs  and  other  factors,  but  within  these  areas 
business  connections  with  B  as  a  rule  grow  closer  the  nearer  it  is 
approached.  Although  it  happens  occasionally  that  B  receives  impor- 
tant imports  from  remote  points,^  so  that  an  inflation  at  B  can  jump 
directly  to  distant  localities  such  as  coal  or  ore  fields,  purchases  and 
sales  nevertheless  decrease  with  distance.  Because  cases  like  these 
are  especially  striking  their  importance  is  apt  to  be  overestimated. 

Analyze  the  expenditures  of  consumers  in  any  given  locality,  and 
see  how  large  a  proportion  goes  to  local  activities  (builders,  retailers, 
artisans,  teachers,  newspapers,  beverages,  and  so  on)  .  The  next 
largest  part  goes  for  goods  from  the  near  vicinity,  the  radius  of 
which  naturally  varies  with  the  size  of  the  town  (greens,  potatoes, 
milk,  eggs,  firewood,  brick,  stone,  and  so  on) .  Another  portion  of  its 
supplies  comes  from  a  greater  hinterland  (cattle  for  slaughter,  fruit, 
butter,  flour,  furniture) ,  while  many  industrial  goods  whose  share 
of  the  total  expenditure  may  be  small  come  from  all  parts  of  the 
country,  and  only  a  small  remainder  of  agricultural  and  industrial 
products  is  imported  from  the  world  at  large.*    The  truth  of  this 

3.  But  only  to  export  them  again  in  the  products  of  local  factories— a  type  of 
finishing  trade. 

4.  B.  Barfod  (Local  Economic  Effects  of  a  Largescale  Industrial  Undertaking 
[Copenhagen  and  London,  1938],  p.  44)  calculated  that  in  Aarhus  45  per  cent  of  con- 
sumption expenditures  (dwelling  up  to  85  per  cent,  clothing  30  per  cent,  food  25  per 
cent)  was  retained  as  local  income.  According  to  Isenberg  ("  Zur  Stadtplanung  in  den 
neuen  deutschen  Ostgebieten,"  Raumforschung  und  Raumordnung,  1941,  p.  137) ,  in  a 
German  agricultural  region  up  to  60  per  cent  of  the  expenditures  of  those  who  are  not 
farmers  will  become  regional  nonagricultural  income  again.  This  he  calls  the  "  intra- 
regional  expenditure  quotient."  For  economic  regions  in  which  industry  and  agri- 
culture are  intermixed  it  would  have  to  be  considerably  higher.  According  to  the  same 
author  (ibid..  Vol.  6,  p.  18) ,  29.3  per  cent  of  German  productive  workers  were 
employed  in  1939  for  local  requirements,  27.3  per  cent  in  agriculture  and  forestry,  and 
27.1  per  cent  in  remaining  industries  (grouped  according  to  regional,  national,  and 
world  markets)  .  If  the  rest  (public  services,  wholesale  trade,  and  communications) 
is  divided  among  these  groups  it  proves  to  be  true  on  the  whole  that  the  demand  of  a 
locality  decreases  absolutely  with  distance. 


270 


Part  Three.     Trade 


becomes  still  clearer  when  it  is  realized  that  the  market  area  around 
B  grows  as  the  square  of  the  distance  from  B.  If  this  is  divided 
into  rings  of  equal  area  it  will  be  found  as  a  rule  that  with  incrasing 
distance  a  constantly  diminishing  fraction  of  the  product  of  each 
ring  is  sold  in  B,  and  a  constantly  smaller  proportion  of  its  purchases 
are  bought  from  B.  This  is  obvious  for  one  and  the  same  product, 
and  especially  for  the  exports  of  B.  It  is  true  also  for  the  imports 
of  B,  since  the  increasing  distance  from  B  even  smaller  localities 
can  carve  out  for  themselves  constantly  growing  supply  areas  from 
the  region  that  supplies  B,  and  since  home  consumption  rises  with 
falling  producers  prices.  But  the  statement  holds  also  for  any  group 
of  products.  It  follows  that  the  effects  of  a  price  change  diminish 
gradually  with  distance  from  its  point  of  origin, 

2.       INCREASING    ABSORPTION     OF     A     CHANGE     IN 
PURCHASING    POWER 

Assume  that  A,  in  Fig.  57,  is  the  man  who  has  ordered  the 
additional  1,000  marks'  worth  of  shoes  from  B^.  C,  E,  G,  and  so  on, 
and  Ci,  jEi,  Gi,  and  so  on,  are  consumers,  and  the  rest  are  producers 
of  one  product  each:  B,  of  shoes;  D,  of  bread;  F,  of  butter,  and  so  on. 
Suppose  that  a  unit  of  each  product  cost  initially  1  mark.  Now  let 
A  disturb  the  equilibrium.  Let  the  chain  of  trade  connections  be  as 
in  the  figure.  Thus  D,  the  baker,  for  example,  would  have  supplied 
C  and  perhaps  E  also,  but  he  would  have  supplied  neither  A  nor  F. 
Such  a  selective  chain  is  the  rule  in  reality  where  imperfect  com- 
petition prevails. 

By  paying  1,000  marks  more  to  Bi,  A  pays  out  that  much  less  as 
a  customer  of  B.  In  order  to  win  a  substitute  buyer,  B  reduces  his 
price  to  one  half.  At  this  price  a  new  customer  C  buys  from  him 
the  1,000  shoes  that  were  not  taken  by  A,  Since  C  now  buys  500 
marks'  worth  more  from  B  than  formerly,  he  must  diminish  his 
purchases  from  D  by  an  equal  amount.  But  in  order  to  sell  his 
500  units  of  bread,  D  will  offer  them  to  E  at  the  reduced  price  of 
80  pfennigs  instead  of  1  mark.  He  need  lower  his  price  less  than 
fi— and  this  is  the  point— because  his  loss  of  sales  amounts  to  only 
500  marks;  not  to  1,000,  as  with  B.  E  buys  375  units  at  80  pfennigs 
each  for  300  marks,  while  C,  for  whom  the  reduced  price  also  holds, 
buys  125  additional  units  of  bread;  which,  to  simplify  the  argument, 
would  reduce  the  value  of  his  purchases  from  D,  despite  the  lower 
price,  by  only  the  500  marks  already  mentioned.  D's  loss  is  reduced 
thereby  from  500  to  200  marks.  And  so  on.  So  much  for  the  spread 
from  B,  the  center  of  the  price  depression. 


Self-Regulation 


271 


Now  for  the  center  o£  the  price  inflation  B^.  As  the  demand  for 
his  shoes  suddenly  increased,  B^  raised  his  price  to  1.5  marks.  C,', 
whose  income  has  not  gone  up,  will  no  longer  buy  1,000  marks 
worth  as  before,  but  only  500  (so  that  B^  will  sell  667  units  to  A 
and  .333  units  to  C,) ,  and  use  the  remaining  500  marks  for  the 
goods  of  Di,  which  so  far  have  not  risen  in  price.  By  joining  D/s 
long-established  customers  with  an  additional  500-mark  demand, 
he  drives  jDi's  prices  up  also,  though  by  less  than  A  Avas  able  to  do 
with  his  additional  purchasing  power  of  1,000  marks  from  B^,  and 
so  on. 


ca  CO 


CO  CO 


-  y 


Fig.  57.  The  spread  of  price  changes.    (Complete  transfer  in  goods  and  an 
elasticity  of  demand  greater  than  1  are  assumed.) 

In  this  way  it  comes  to  pass  that  with  distance  from  the  center 
of  origin  both  the  fall  in  purchasing  power  and  prices  (starting 
with  B)  and  the  increase  in  purchasing  power  and  prices  (starting 
with  jBi)   will  flatten  out.^ 


5.  This  conclusion  is  reached  under  the  most  probable  assumption  for  these  con- 
ditions: that  the  elasticity  of  demand  is  greater  than  unity.  If  the  elasticity  everywhere 
were  equal  to  I,  B  or  B^  would  suffer  all  the  loss  or  gain  all  the  profits  no  matter  how 
they  set  their  prices.  If  B  and  B^  each  are  several  producers  competing  with  one 
another,  an  elasticity  of  demand  of  less  than  unity  is  conceivable;  (if  each  represents 
but  one  producer,  an  elasticity  of  demand  of  less  than  unity  implies  that  he  failed  to 


272 


Part   Three.     Trade 


3.      THE    DISSIPATION     OF     PURCHASING    POWER 

So  far  we  have  assumed  that  the  shifted  demand  of  A  fell 
entirely  on  seller  B,  who  in  turn  could  gain  only  one  new  customer 
C  as  a  substitute.  But  in  reality  A  will  reduce  his  purchase  from 
several  sellers,  and  B  will  gain  several  new  customers.^  Thus  the 
reduced  demand  will  affect  the  individual  seller  less  and,  in 
addition,  he  need  not  lower  the  price  so  much  to  dispose  of  his 
unsold  goods.  This  dissipation  increases  in  geometrical  progression, 
whereas  the  distance  from  the  origin  of  the  disturbance  increases 
only  in  arithmetical  progression.  The  price  change  therefore  dies 
out  in  space  even  more  quickly  than  we  should  have  had  to  assume 
from  the  foregoing  argument. 

4.      THE     INCREASING    TRANSFER     OF     GOODS 

The  three  causes  thus  far  described  cause  a  price  wave  to  flatten 
out  with  increasing  distance  from  its  origin  because  it  divides.  In 
so  far  as  a  more  and  more  extensive  transfer  of  goods  takes  place, 
as  the  two  price  waves  approach  one  another,  they  flatten  out 
because  they  disappear.    This  will  be  described  below. 

B.    The  End  of  the  Price  Waves 

Whereas  local  price  differences  are  very  great  in  the  first  eco- 
nomic period,  the  fall  in  prices  widens  and  flattens  out  in  the 
succeeding  ones.  It  must  be  remembered,  however,  that  so  far  as 
the  causes  of  this  phenomenon  (discussed  under  1  to  3)  extend, 
the  sum  of  the  increases  or  decreases  in  purchasing  power  remains 
the  same,  even  though  it  is  divided  among  more  and  more  persons 
by  partial  shifting.  This  is  the  law  of  the  conservation  of  purchasing 
power.  Thus,  though  the  total  fall  in  purchases  from  B,  say,  was 
1,000,  he  suffers  a  loss  of  only  500  marks  and  through  a  price  cut 
shifts  the  further  loss  of  500  to  D,  who  in  turn  absorbs  200  marks 
of  it  and  passes  on  a  loss  of  300.  The  sum  of  the  amounts  absorbed 
(500  +  200  4-90  +  40  +  -  •  •)     is    exactly    1,000.     The    shift   from 


set  his  price  at  Cournot's  point)  .  In  this  rather  improbable  case  the  movement  of 
prices  may  be  exactly  the  reverse  of  that  described  in  the  text:  upward  with  B,  down- 
ward with  B^.  At  best  B  could  shift  the  entire  loss  to  D;  at  the  worst,  B^  would  have 
to  transfer  all  the  profits  to  D^,  until  at  last  profits  and  losses  reached  Z  and  were 
equalized  there.  The  effect  of  a  combination  of  different  elasticities  is  still  more  com- 
plicated and,  for  a  general  discussion,  still  less  interesting. 

6.  Here  we  speak  of  dissipation  within  groups  of  buyers  and  sellers,  whereas  in  2 
dissipation  between   (individual)    buyers  and  sellers  was  discussed. 


Self-Regulation  273 

income  period  to  income  period  is  to  be  distinguished  from  this 
shift  from  person  to  person.  If  in  the  second  period  A  were  to  buy 
his  shoes  again  from  B  as  usual,  the  latter  would  nevertheless  have 
received  500  marks  less  in  the  first  period  with  which  to  buy  leather 
from  Z.  B's  loss  therefore  consists  in  the  curtailment  of  his  pur- 
chases from  Z,  and  once  he  has  dealt  with  this  loss  the  storm  has 
passed  him.^-^    But  now  the  cloud  hangs  over  Z.® 

The  disturbance  would  be  carried  over  from  one  income  period 
to  the  next  and  continue  to  claim  new  victims,  were  it  not  gradually 
dissipated  in  two  different  ways.  The  compensatory  absorption 
about  to  be  described  must  not  be  confused  with  the  damaging 
absorption  already  discussed.  The  latter  reappears  again  and  again, 
and  if  the  other  did  not  intervene  (that  is,  if  we  dealt  with  a  closed 
economic  system)  it  would  come  to  an  end  only  with  a  general  and 
uniform  price  reduction  in  the  region  in  which  the  purchasing 
power  has  fallen.  The  former  is  final.  The  manner  in  which  it 
appears  first,  though  not  most  frequently,  is  this.  j5i,  for  example, 
with  his  increased  income,  wishes  to  buy  from  Z  exactly  what  B 
had  to  give  up  because  of  his  reduced  purchasing  power.  In  this 
case  Z's  prices  remain  unchanged.  But  such  a  prompt  agreement 
between  increased  and  decreased  demand  is  hardly  to  be  expected.^" 
As  a  rule  there  would  start  from  jB  as  a  producer  not  only  the  series 
of  price  drops  illustrated;  from  him  as  a  consumer  with  500  marks' 
less  purchasing  power  there  would  start  also  a  corresponding  series 
of  price  drops  that  is  not  shown  in  the  figure.  The  same  would  be 
true  for  D,  with  his  200-mark  reduction  in  purchasing  power,  and 
so  on.  Buyers  B,  D,  F,  H,  and  so  on,  would  pass  on  together  to  Z 
a  purchasing  power  reduced  by  up  to  1,000  marks;  not  directly, 
of  course,  but  through  chains  of  intermediaries.   Z  must  exist  some- 

7.  Thus  B  has  shifted  when  he  has  sold  500  marks'  worth  more  of  merchandise  to 
C,  even  though  at  a  loss,  and  bought  500  marks,  worth  less  from  Z.  Then  he  enters 
the  next  production  period  with  exactly  as  much  purchasing  power  as  he  had  in  the 
preceding  one.  Unless  part  of  the  loss  in  purchasing  power  still  affects  one  of  his 
customers,  the  transfer  is  over  as  far  as  he  is  concerned. 

8.  In  the  case  of  single  disturbances,  therefore,  we  deal  with  a  true  wave,  not  simply 
with  a  price  gradient. 

9.  Here  two  situations  must  be  distinguished.  The  drop  in  purchasing  power  shows 
again  at  an  increasingly  distant  place  during  every  new  economic  period,  but  within 
one  and  the  same  period  its  effect  is  exhausted  as  soon  as  all  goods  have  been  sold, 
even  though  in  part  at  reduced  prices. 

10.  It  is  still  more  improbable  that  B^  should  obtain  his  increased  requirement 
directly  from  B.  As  a  general  rule  B  would  endeavor  to  dispose  of  his  stock  by  trading 
with  a  third  person,  and  B^  would  try  to  replenish  his  in  the  same  way. 


274  P'^^^  Three.     Trade 

where,  however;  that  is,  there  must  be  one  or  several  places  where 
diminished  and  increased  purchasing  power  balance  one  another 
without  altering  prices. 

Besides  this  there  is  still  another  possibility,  more  probable  at 
first:  That  Z)i  and  Fa,  with  their  combined  additional  purchasing 
power  of  300  marks,  will  become  new  customers  not  o£  Z,  but  of  D, 
in  place  of  E.  The  series  will  then  stop  with  D  and  the  price  drop 
will  no  longer  reach  F,  H,  and  so  on.  Consequently  their  demand 
from  Z  will  not  decrease,  which  equalizes  Z's  loss  of  an  additional 
demand  from  D^  and  F^  previously  assumed.  In  other  words,  these 
two  simultaneous  possibilities  of  a  link  between  chains  of  price 
increases  and  price  decreases  mean  that  those  who  gain  in  pur- 
chasing power,  either  as  a  simple  result  of  its  shift  (through  Z)  or 
after  a  preceding  price  change  (in  the  case  of  D,  for  instance) , 
demand  what  the  persons  with  reduced  purchasing  power  have 
given  up.  Both  are  typical  examples  of  the  real  transfer,  which  is 
achieved  when  decreased  and  increased  purchasing  power  meet 
somewhere. 

The  spatial  distribution  of  these  two  forms  of  transfer  is  impor- 
tant. At  first  those  persons  or  places  with  decreased  purchasing 
power  dp  and  those  with  increased  purchasing  power  ip  may  be  so 
far  apart  that  no  equalization  occurs  at  all.  But  as  the  waves  of 
purchasing  power  spread  dp  and  ip  move  closer  together.  At  first 
only  their  largest  supply  and  market  areas  overlap  slightly,  and  the 
shift  in  demand  from  ip  to  dp  of  those  few  in  the  region  of  overlap 
Z  can  influence  their  prices  but  little.  Consequently  only  a  slight 
real  transfer  occurs  at  first  at  sharply  altered  prices.  Gradually  the 
overlaps  increase  and  dp  and  ip  even  move  into  each  others'  areas, 
so  that  a  direct  real  transfer  develops  at  prices  that  are  very  much 
less  changed.  At  last  dp  and  ip  coincide  with  Z,  and  the  final 
transfer  is  completed  at  unchanged  prices.  With  time,  that  is,  as 
the  waves  of  purchasing  power  spread,  the  localities  between  which 
the  real  transfer  takes  place  approach  one  another,  the  transfer 
increases  in  extent,  and  the  prices  at  which  it  occurs  depart  less 
and  less  from  the  normal  ones. 

The  territory  involved  in  the  real  transfer  does  not  as  a  rule 
coincide  entirely  with  the  areas  of  increased  and  decreased  pur- 
chasing power,  but  lies  necessarily  within  their  borders.  The  real 
transfer  takes  place  between  parts  of  areas  with  decreased  and 
increased  purchasing  power. 


Self-Regulation  275 

§3.     Economic   Landscapes 

The  economic  connections  of  an  enterprise  are  not  the  same  in 
all  directions;  on  the  contrary,  it  is  generally  situated  in  an  economic 
landscape  toward  whose  center  it  is  oriented.  This  is  not  without 
influence  on  the  spread  of  price  waves.  Although  the  movement  of 
prices  always  remains  especially  pronounced  about  its  origin,  the 
central  points  of  economic  landscapes  reflect  local  changes  anywhere 
in  the  hinterland  relatively  early  and  strongly;  on  the  one  hand, 
via  the  whole  area;  on  the  other,  the  movement  jumps  from  these 
central  points  to  those  of  neighboring  landscapes,  which  thus  are 
exposed  not  only  at  their  borders  but  at  their  centers  as  well.  That 
is  to  say,  they  are  exposed  throughout.^^ 

This  important  function  of  economic  capitals,  the  transfer  of 
price  fluctuations  (of  a  cyclical  nature  also)  to  their  economic 
landscapes  or,  conversely,  from  these  to  the  rest  of  the  world,^^ 
becomes  still  more  clear  when  it  is  recalled  that  the  final  money 
transfer  takes  place  as  a  rule  through  central  banks,  not  directly 
between  those  concerned.  If,  therefore,  there  is  any  logic  at  all  in 
the  substitution  of  simplifying  spatial  constructs  for  the  individuals 
who  are  really  the  ones  affected  by  disturbances  of  trade,  these  con- 
structs should  certainly  be  economic  regions  [rather  than  countries], 

§4.     Countries 

Do  disturbances  in  economic  relations  always  exhaust  themselves 
in  the  described  effects  on  those  first  concerned  and  by  spreading 
through  the  channels  of  their  originators'  business  connections,  or 
are  special  phenomena  added  when  payments  have  to  be  made 
across  national  boundaries?  We  must  now  examine  the  significance 
of  political  boundaries  for  the  overcoming  of  temporary  disturbances 

11.  This  is  really  a  special  case  of  Huygens'  principle,  according  to  which  every 
point  in  a  wave  may  become  the  center  of  a  new  wave. 

12.  Individual  industries  in  a  landscape  will  of  course  also  maintain  direct  connec- 
tions with  the  outer  world,  and  a  machine  factory,  for  example,  will  feel  a  cyclical 
revival  in  other  regions  more  by  way  of  industrial  areas  or  its  particular  circle  of 
customers  than  through  the  capital  of  its  own  region.  This  is  even  more  obvious  where 
there  is  no  organized  landscape  at  all.  When  a  town  has  but  little  connection  with  its 
landscape,  a  local  improvement  in  its  economy  cannot  spread  through  the  region  but 
must  be  dispersed  here  and  there.  This  need  not  mean  its  complete  dissipation,  for 
the  arming  of  a  fort,  say,  may  at  first  chiefly  benefit  one  single  factory  somewhere  in  a 
region  of  heavy  industries;  but  it  does  mean  an  irregular  geographical  distribution, 
which  of  course  may  suffice  to  rob  it  of  the  cumulative  cyclical  effect  which  otherwise 
would  occur  in  the  course  of  interregional  trade. 


376  Part  Three.     Trade 

of  equilibrium;  not  their  significance  for  the  equilibrium  itself, 
since  that  has  already  been  discussed.  In  so  far  as  countries  coincide 
approximately  with  economic  regions,  either  fortuitously  or  by  com- 
pulsion, what  has  already  been  said  of  them  holds  here  also.  Has 
the  state  as  such,  not  as  an  economic  area,  additional  significance? 

a.    Currency 

Differences  in  currencies  are  the  first  important  characteristic  of 
international  trade.  Differences  in  monetary  policies  will  form  the 
subject  of  the  next  chapter;  here  the  question  is  whether  differences 
in  the  fundamental  construction  of  currencies  alter  the  transfer 
mechanism.  But  first  we  shall  separate  from  this  problem  a  more 
basic  one. 

I.   THE  SIGNIFICANCE  OF  THE  FACT  OF  CREDIT  CREATION 
FOR  THE  TRANSFER 

Since  large  payments  are  almost  never  made  directly,  but 
generally  through  banks,  we  could  have  asked  long  ago  what  is 
changed  in  the  process  of  transfer  so  far  described  when  banks 
create  credit.  But  this  question  has  been  postponed  in  order  to 
discuss  it  together  with  the  influence  of  a  modern  monetary  system 
on  transfer. 

Suppose  the  monetary  system  were  such  that  on  the  basis  of  the 
money  generally  acceptable  between  debtors  and  creditors  (gold 
or  other  international  means  of  payment,  bank  notes  or  deposits 
with  the  central  bank  for  trade  within  a  country)  a  greater  amount 
in  not  universally  accepted  money  ^^  (bank  notes  and  bank  deposits 
in  international,  bank  deposits  also  in  domestic  trade)  could  be 
created  that  would  circulate  only  within  the  central  area  of  the 
debtor's  or  creditor's  bank.  Then  a  debtor  might  pay  a  foreign  debt 
in  money,  but  not  necessarily  in  internationally  accepted  money,  so 
that  the  creator  of  the  local  money  would  still  face  the  problem  of 
procuring  the  rest  of  the  international  money.  In  this  case  the  final 
transfer  described  above  is  preceded  by  a  preliminary  transfer,  the 
results  of  which  are  later  nullified  by  a  reaction. 

(aa)  Preliminary  Transfer.  The  preliminary  transfer  is  brought 
about  by  a  further  price  movement,  which  is  added  to  that  caused 
by  a  shift  in  purchasing  power. 

13.  I  shall  call  a  medium  of  payment  that  is  valid  only  within  a  spatially  or  other- 
wise restricted  group  "  local  money." 


Sclf-Regidnlion  -  277 

First:  Shifting  of  the  Price  Level.  An  additional  and  general 
price  drop,  somewhat  sharper  about  its  source,  however,  will  occur 
in  the  area  of  those  banks  that  have  received  the  amount  to  be 
transferred  in  credit  money,  whereas  they  themselves  have  to  remit 
in  monetary  reserves."  There  is  first  the  local  bank,  which  receives 
the  amount  in  its  own  deposits  and  pays  it  out  again  in  money 
serving  as  regional  means  of  payment. ^^  Another  is  the  regional 
bank,  which  has  to  change  its  deposits  into  notes;  finally,  the  central 
bank,  which  receives  notes  and  has  to  pay  out  gold.  Suppose  a 
unilateral  payment  of  1,000  marks  has  to  be  made  from  Stuttgari  to 
Paris.  And  suppose  that  in  Germany  gold  is  not  the  only  medium 
of  payment  but  that  there  arises  on  it  a  superstructure  of,  say,  twice 
as  many  notes,  on  the  basis  of  which  a  tenfold  amount  of  deposits 
will  be  created.  If  the  Reichsbank  sends  1,000  marks  in  gold  to 
Paris  it  must  collect  twice  as  much  in  bank  notes  by  raising  its 
discount  rate  (assuming  that  only  the  minimum  reserves  are  kept 
at  all  times) .  The  credit  basis  for  the  Bank  of  Wiirttemberg, 
which  sent  1,000  marks  in  notes  to  Berlin,  has  shrunk  even  more. 
It  must  reduce  the  amount  of  deposits  by  10,000  marks,  either  by 
raising  its  rediscount  rates  or  by  direct  curtailment  of  credits.  Con- 
sequently prices  in  Wiirttemberg  fall  ten  times  more  than  if  there 
were  no  deposits,  and  in  Germany  twice  as  much  as  if  there  were 
no  bank  notes.  This  true  shifting  of  the  price  level  occurs  only 
with  credit  creation;  that  is,  with  a  hierarchy  of  different  kinds  of 
money,  whereas  in  a  region  with  a  uniform  currency  the  price  waves 
started  by  a  shift  in  purchasing  power  necessarily  suffice  for  transfer.^^ 

Second:  Effects  up  to  the  Due  Date  (Immediate  Partial  Transfer). 
The  change  in  relative  price  level  will  not  go  so  far,  however,  for 
it  is  counteracted  by  the  increasing  export  surplus  that  it  is  supposed 
to  bring  about.  But  gold  shipments  exceed  nevertheless  what  would 
be  required  merely  to  cover  the  price  waves.   Thus,  if  only  50  marks 

14.  If  some  time  passes  between  the  creation  of  the  deposit  and  its  disposition, 
there  arises  the  additional  problem  of  whether  the  banks  will  intervene  in  the  transfer 
with  short-term  loans  of  the  idle  amount.  In  this  way  the  debtor's  bank  could  counter- 
act the  local  deflation  that  he  has  caused,  and  the  creditor's  bank  could  anticipate  the 
local  price  inflation.  But  this  would  be  wise  bank  policy  only  when  it  was  certain  that 
the  owner  would  not  first  dispose  of  his  deposit;  that  is,  if  no  further  transfer 
threatened. 

15.  For  example,  a  transfer  of  reserves  with  the  local  Federal  Reserve  Bank  from 
one  commercial  bank  to  another  within  the  same  Federal  Reserve  District.— W.  F.  S. 

16.  Not  only  money  rates,  but  all  prices  must  have  at  least  the  same  tendency;  not 
merely  some,  as  with  price  waves.  In  this  case  the  change  in  the  price  level  is  a  reality 
instead  of  only  a  fictitious  average,  as  with  price  waves. 


2y8  P^^f^  Three.     Trade 

in  gold  were  sent  to  France,  on  the  basis  of  which  1,000  marks  in 
deposits  would  be  created  there  and  destroyed  in  Germany,^'  950 
marks'  worth  of  goods  would  still  have  to  be  transferred.  But  this 
is  impossible  at  this  price  level  as  long  as  the  two  price  waves  are 
still  in  the  neighborhood  of  Stuttgart  and  Paris.  On  the  contrary, 
Germany  can  pay  punctually  only  if  more  than  50  marks  in  gold  go 
to  France.  In  anticipation  of  this  the  Reichsbank  raises  its  discount 
rate,  which  immediately  lowers  the  German  price  level  up  to  the 
frontier.  For  opposite  reasons  the  Bank  of  France  will  just  as  quickly 
force  a  general  increase  in  prices.  Whereas  the  price  waves  approach 
one  another  slowly,  the  areas  of  falling  and  rising  price  levels  meet 
almost  instantaneously  (at  least  with  neighboring  countries) .  This 
causes  a  rapid  and  considerable  transfer  of  goods,  which  probably 
takes  place  chiefly  in  the  border  regions.  We  shall  disregard  the 
capital  movements  that  also  are  released  and  assume  that  700  marks 
in  gold  and  300  in  merchandise  are  transferred  at  first,  which  must 
be  paid  when  the  German  payment  comes  due. 

Third:  Effects  After  the  Due  Date  (Early  Total  Transfer) . 
Although  the  disturbing  payment  has  now  been  completed,  the 
transfer  is  by  no  means  finished.  For  the  price  shifts  still  continue: 
the  price  waves  because  they  are  still  too  far  apart  to  neutralize 
one  another  entirely,  and  the  relative  shift  in  price  levels  because 
there  are  still  700  marks  in  German  gold  in  France.  As  long  as 
the  change  in  the  German  relative  to  the  French  price  level  persists, 
the  German  export  surplus  will  continue  beyond  the  original  due 
date.  But  now  it  must  be  paid  by  France  in  cash  since  the  1,000 
marks  have  long  since  been  paid,  partly  in  gold  and  partly  in  goods; 
that  is,  all  but  50  marks  of  the  German  gold  flows  back  from  France, 
price  levels  return  to  their  former  height,^^  the  German  export 
surplus  dries  up,  and  after  a  further  650  marks'  worth  of  goods  has 
been  shipped  the  transfer  of  goods  appears  completed. 

(bb)  The  Final  Transfer.  But  the  price  waves  started  around 
Paris  and  Stuttgart  by  the  shift  in  purchasing  power  are  still  on 
their  way,  and  approach  one  another.  Even  during  this  process 
they  are  partially  equalized,  and  completely  so  when  they  meet,  as 
has  already  been  described.    This  levelling  off  of  increased  and 

17.  Thus  a  gold  shipment  to  this  extent  has  no  further  influence  on  prices  in 
addition  to  that  of  the  transfer  of  purchasing  power. 

18.  Only  mathematically  is  the  French  price  level  slightly  higher  than  before 
because  of  the  continued  increase  in  the  amount  of  money  by  1,000  marks;  and  vice 
versa  for  the  German  price  level. 


Sclf-Regululion  279 

decreased  purchasing  power  represents  the  genuine  transfer  of  goods 
that  takes  place  in  any  case,  whereas  a  preliminary  transfer,  which 
must  be  sharply  distinguished  from  it,  is  added  only  with  a  certain 
type  of  monetary  system.^" 

(cc)  The  Reaction.  Thus  950  marks  in  goods  were  transferred 
twice:  the  first  time  as  the  result  of  the  change  in  relative  price 
levels,  the  second  with  the  neutralizing  of  the  price  waves.  Thus 
there  is  one  transfer  too  many.  If  France  orders  an  additional  1,000 
marks'  worth  of  German  products  when  one  of  the  two  waves  crosses 
the  frontier,  she  would  have  to  pay  partly  in  gold  and  partly  in 
goods,  and  finally  up  to  50  marks  in  the  former  and  950  in  the  latter. 
Hence  exactly  as  much  French  gold  flows  temporarily  into  Germany 
as  she  lost  of  her  own  gold  in  the  beginning,  except  for  those  50 
marks,  which  cover  the  price  waves;  this  gold  movement  alone  is 
not  reversible,  because  the  price  waves  are  not.  Thereupon  the 
German  price  level  rises  above  the  French  by  as  much  as  it  was 
below  this  before.  So  in  the  final  settlement  the  exact  mirror  image 
of  the  original  preliminary  transfer  is  repeated.  Later  the  whole 
process  is  again  undone.  Although  technically  necessary  with  credit 
creation  (when  it  resulted  in  redeemable  local  money) ,  in  a 
deeper  sense  it  was  superfluous.  The  preliminary  transfer  and  the 
subsequent  reaction  cancel  out,  and  neutralization  of  the  waves  of 
purchasing  power  remains  the  sole  essential  feature  in  the  entire 
transfer. 

2.     THE    SIGNIFICANCE    FOR    TRANSFER    OF    THE    EXTENT    OF 
CREDIT    CREATION,    AND    OF    DIFFERENCES    IN    CURRENCY 

(aa)  Various  Possibilities  in  the  Construction  of  Currencies. 
Where  local  money  has  but  little  international  means  of  payment 
as  cover  (as  with  credit  creation) ,  or  none  at  all  (as  with  paper 
currencies) ,  payment  on  the  due  date  offers  a  special  problem  for 
the  debtor  as  well  as  for  the  debtor  country,  which  is  solved  by  the 
preliminary  transfer.  We  shall  now  compare  it  for  the  whole  scale 
from  complete  to  zero  cover,  always  under  the  assumption  that  the 

19.  Additional  local  money  must  be  created,  which  is  redeemable  in  generally 
accepted  money.  The  local  money  must  be  additional,  at  least  in  part;  it  must  not 
simply  replace  international  money.  The  additional  money  must  be  local  money. 
The  creation  of  more  generally  accepted  money  has  different  effects.  The  local  money 
must  be  redeemable,  otherwise  there  arises  no  necessity  to  destroy  it.  Though  not 
necessary,  it  is  usual  tor  this  creation  of  local  money  to  take  place  in  the  process  of 
credit  creation. 


28o  Part  Three.     Trade 

currencies  of  debtor  and  creditor  countries  are  similarly  constructed 
and  that  the  reserve  ratio,  like  the  exchange  rate,  is  strictly 
maintained. 

Suppose  once  more  that  1,000  marks  are  to  be  sent  from  Stuttgart 
to  Paris.    (I)   If  transfers  are  made  in  hoarded  gold  and  the  receiver 
hoards  it  in  turn,  no  price  fluctuation  will  be  necessary.^"     (II)    If 
the  local  money  is  100  per  cent  covered  by  gold  in  both  countries, 
but  this  time  the  amount  owed  has  to  be  withdrawn  from  circu- 
lation, both  price  waves  due  to  the  shift  in  purchasing  power  will 
be  started;  the  immediate  payment,  however,  will  likewise  be  made 
at  first  almost  entirely  in  gold,  into  which  the  local  money  accumu- 
lated  by   the   debtor   can   be   converted   without   further   trouble. 
(Ill)    If  there  is  a  10  per  cent  bank-note  coverage  behind  deposit 
money  and  the  bank  notes  in  turn  are  fully  covered  by  gold,  we 
have  the  typical  case  of  intranational  trade,  already  described  above, 
also  in  international  trade.    Now  the  local  money  can  no  longer  be 
simply  converted  into  gold;  on  the  contrary,  gold  shipment  reacts 
tenfold  on  the  amount  of  deposits.    To  the  extent  of  10,000  marks 
the  creation  of  local  money  must  be  reversed  in  the  one  country 
and  brought  about  in  the  other.    A  shift  in  the  price  level  takes 
place  in  addition  to  price  waves.    Perhaps  200  marks  will  now  be 
transferred  in  goods,  and  only  the  remainder  in  gold.     (IV)    if  the 
gold  cover  of  the  notes  is  only  50  per  cent  a  gold  shipment  of  800 
marks  will  change  the  amount  of  notes  by   1600  marks  and  the 
amount  of  deposits  by   16,000  marks.    Price  levels  will  shift  still 
more  than  in  the  preceding  case,  because  the  remainder  that  is  paid 
in  gold  has  twenty  times  the  effect  on  the  monetary  circulation. 
Whereas  in  the  first  case  1,000  marks  were  transferred  in  gold,  in 
the  second  almost  1,000,  and  in  the  third  at  least  800,  it  is  now 
perhaps  700  marks.     (V)   With  a  pure  paper  currency  no  monetary 
gold  will  be  shipped;  on  the  contrary,  the  1,000  marks  will  have  to 
be  sent  entirely  in  goods  up  to  the  due  date.   Moreover,  there  occurs 
the  greatest  shift  in  price  levels  that  can  accompany  the  transfer 
of  this  amount. 

Decreasing  reserve  ratios  or,  which  amounts  to  the  same  thing, 
increasing  the  creation  of  local  money,  therefore  means  a  growing 
risk  that  this  creation  will  have  to  be  temporarily  reversed. ^^   There 

20.  This  is  immediately  true  when  gold  flows  from  the  hoard  of  the  debtor  to  that 
of  the  creditor.  If  it  flows  from  the  hoard  of  one  to  that  of  another  bank  of  issue  it  is 
true  only  when  both  neutralize  the  effects  of  the  shift  in  purchasing  power  by  their 
credit  policy. 

21.  It  is  therefore  no  meaningless  caprice  of  the  currency  mechanism  when  countries 


Self -Regulation  281 

is  but  one  alternative:  a  fluctuating  exchange  rate.  Then  the  relative 
change  in  prices  takes  place  through  this  instead  of  directly.^^--^ 

As  paper  currencies  are  conceivable  also  without  credit  creation 
and  as  fluctuations  in  the  price  level,  either  directly  or  through  the 
exchange  rate,  are  especially  pronounced  with  paper  currencies,  their 
causes  must  lie  even  deeper  than  we  have  been  assuming  until  now. 
They  consist  in  currency  differences  in  the  widest  sense;  that  is,  in 
the  fact  that  all,  or  at  least  the  created,  means  of  payment  of  the 
one  banking  area  are  invalid  in  that  of  another  bank.^*  Thus  there 


with  low  reserve  ratios  have  to  resign  themselves  to  wide  price  fluctuations.  This  is  the 
natural  drawback  of  their  extensive  creation  of  credit. 

22.  This  would  not  contradict  in  the  least  our  assumption  of  a  fixed  reserve  ratio. 
For  whether  the  amount  of  local  money,  and  with  it  the  price  level,  is  lowered  by 
one  tenth  because  of  a  gold  loss  of  10  per  cent  of  the  reserve,  or  whether  the  price  of 
gold,  expressed  in  local  money  is  raised  by  one  tenth  (for  a  10  per  cent  depreciation 
can  mean  only  this)  so  that  the  physically  diminished  gold  reserve  will  regain  its 
former  nominal  value  and  the  amount  of  local  money  can  thus  be  left  unchanged,  the 
actual  reserve  ratio  is  the  same  in  both  cases.  We  must  accustom  ourselves  to  the  idea 
that  the  individual  features  of  the  old-fashioned  gold  standard,  such  as  fixed  reserve 
ratios  and  exchange  rates,  do  not  necessarily  go  hand  in  hand.  (See  my  article,  "  Die 
Lehre  vom  Transfer— neu  gefasst,"  Jahrbiicher  fiir  Nationalokonomie,  CLIV  [1941],  395, 
note  1)  .  Paper  currencies  too  (no  reserves)  may  be  accompanied  by  fixed  or  fluc- 
tuating exchange  rates. 

23.  The  difference  appears  especially  in  the  difficulties  of  transfer.  When  a  creditor 
country  buys  nothing  from  a  debtor  country  in  spite  of  an  enormous  drop  in  the 
exchange  rate,  the  latter  cannot  pay  if  the  debt  exceeds  its  gold  supply,  but  its  economy 
goes  on  as  though  nothing  had  happened.  With  fixed  exchange  rates,  on  the  other 
hand,  the  debtor  country  will  be  bankrupt,  not  only  externally,  but  also  at  home 
because  of  the  severe  deflationary  crisis.  It  is  clear  that  the  cause  of  transfer  difficulties 
lies  in  sales  alone.  With  dissimilar  currencies  they  appear  earlier,  to  be  sure,  and  the 
smaller  the  reserve  ratio,  the  greater  are  their  secondary  deflationary  effects  because 
the  fewer  the  installments  that  can  be  paid  at  first  out  of  the  supply  of  international 
means  of  payments,  the  more  the  gold  drain  alters  the  amount  of  local  money.  The 
more  inflexible  the  reserve  ratio,  here  more  quickly  the  secondary  effects  begin  to 
appear,  but  they  are  avoidable  with  variable  exchange  rates  and  thus  not  to  be 
ascribed  to  the  currency  difference  itself.  Only  for  fixed  exchange  rates  does  F.  W. 
Meyer  {Der  Ausgleich  der  Zahlungsbilanz  [Jena,  1938],  p.  Ill)  correctly  make  the  dis- 
tinction that  the  gold  cover  may  be  insignificant  for  restraining  the  creation  of  money 
but  that  for  international  payments,  on  the  contrary,  its  size  must  be  appropriate  to 
the  gravity  of  the  disturbances.  Moreover,  even  with  the  old-fashioned  gold  standard, 
thanks  to  fluctuations  between  the  gold  points,  price  fluctuations  will  be  replaced  at 
least  in  small  part  by  fluctuations  in  the  exchange  rate,  an  advantage  that  would  be 
abolished  by  international  clearing  through  BIS  (Bank  for  International  Settlements) , 
as  W.  Sulzbach  has  emphasized  ("  Der  wirtschaftliche  Begriff  des  Auslands,"  Weltwirt- 
schaftliches  Archiv,  XXXII  [1930],  p.  75)  . 

24.  Hence  one  must  think  here  not  only  of  the  bank  notes  of  various  countries,  but 
also  of  differences  within  countries.  For  instance,  the  notes  of  Federal  Reserve  Banks 
in  the  United  States  are  returned  to  the  issuer  when  they  reach  another  Federal  Reserve 


282 


Part  Three.     Trade 


is  a  slow  transition  between  gold  and  paper  currency.  The  greater 
the  supply  of  international  means  of  payment  {gold  cover) ,  the 
smaller  are  price  fluctuations  at  first  and  the  greater  the  movement 
of  gold,  and  vice  versa  (Table  15)  .^^-^^ 


Table   15 


Construction  of  Currency 


Preliminary  Transfer  by 


Gold  cover 
of  notes 


Note 
circu- 
lation 


Deposits 

(fractional) 

reserves 

by  notes) 


Gold 
movement 


Price 
movement 


II 


Excess 


III 


IV 


Gold 
currency 


100% 


V        Paper  currency 


100% 


Immaterial 


Zero 


No 


^  Yes 


99-1% 


!>Yes 


Zero 


These  differences  lose  some  of  their  significance,  however,  since 
in  all  cases  even  the  preliminary  transfer  must  be  made  in  goods. 
As  a  consequence  price  changes  are  more  lasting  the  smaller  they 
are;  that  is  to  say,  it  takes  all  the  longer  for  the  great  stream  of  gold 
to  flow  back  again.  The  sole  remaining  difference  between  transfer 
with  dissimilar  and  similar  currencies  is  that  with  the  former  (paper 
currency)  the  transfer  takes  place  immediately  in  goods,  whereas 
with  partial  (gold  currencies)  or  complete  similarity  (intranational 
trade  or  a  world  currency)    it  is  distributed  over  a  longer  period. 


District.  This  was  the  case  also  with  the  notes  of  the  Bavarian  and  Wiirttemberg  banks 
of  issue.  The  deposit  money  of  a  bank  is  invalid  outside  the  circle  of  its  customers. 
Conversely,  the  circulating  media  of  different  currency  systems  may  have  equal  value 
in  practical  dealings.  Thus  American  bills,  and  to  some  extent  Canadian  as  well,  are 
usually  accepted  at  face  value  throughout  a  rather  wide  zone  along  the  border,  and 
the  coins,  in  particular,  of  both  countries  are  so  similar  that  they  can  be  used  in  slot 
machines  on  either  side  of  the  line. 

25.  Poor  nations  that  can  afford  only  a  small  gold  cover  therefore  do  well  to  go 
over  to  "  free  "  rates  of  exchange,  which  render  the  wide  price  fluctuations  consider- 
ably less  harmful. 

26.  There  is  a  second  and  different  reason,  based  only  on  frictional  difficulties,  why 
price  fluctuations  are  smaller  with  a  high  gold  cover.  As  the  shift  in  the  prices  of 
goods  and  the  reaction  of  foreign  trade  to  it  require  time,  whereas  nominal  transfer 
must  take  place  immediately,  in  all  cases  the  largest  part  of  the  payment,  neglecting 
short-term  captital  movements,  will  be  transferred  at  first  in  gold  until  the  transfer 
of  goods  begins.  Btit  approximately  the  same  gold  movement  has  less  effect  with  a 
higher  than  with  a  lower  gold  cover.  For  this  reason  a  high  gold  cover  is  more  favor- 
able with  fixed  exchanges. 


Self-Regtilatjon 


283 


The  shift  in  price  levels  in  the  first  case  is  therefore  sharper  and 
shorter,  in  the  second  weaker  but  more  lasting.  In  brief,  the  more 
uniform  the  currency,  the  more  slowly  preliminary  transfer  in  goods 
takes  place." 

(bb)  Creditor  and  Debtor  Countries  Have  Differently  Con- 
structed Currencies.  When  the  degrees  of  cover  are  unequal,  the 
actual  shift  in  price  levels  and  the  effect  on  each  country,  varies 
with  the  degree  of  cover.-^  Table  16  shows,  first,  what  we  have 
already  seen  in  the  last  section:  That  the  higher  the  gold  coverage 
with  one  participant  in  a  transaction,  or  even  with  both,  the  larger 
the  portion  of  the  resulting  payment  through  gold  movement  alone. 

Table    16.   TRANSFER   WITH   DIFFERENT   RESERVE   RATIOS 


1 


Note 

Coverage  in 

Gold,  % 

A  B 


Gold  Shipment, 

Marks  from 

A  toB 


Price 
Fluctuation 

% 
A  B 


Price 
DiflFerence 
B  over  A 

% 


10 
10 
40 
30 
40 


10 
40 
10 
50 
40 


^ 


200 
260 
300 
490 
500 


-20 
-26 
-  8 
-16 
-12 


+20 
+  7 
+30 
+  10 
+  12 


A 


50 
44 
41 
31 
28 


Explanation:  Column  2:  The  order  of  magnitude,  but  not  its  gradation,  is  arbitrary. 
Column  3:  A  total  note  circulation  of  10,000  marks  in  each  country  is 
assumed.    Deposits  are  supposed  to  be  nonexistent.    Country 
A  and  Country  B  are  supposed  to  be  equally  large. 

The  table  shows  further  that  when  only  one  of  the  participants 
(cases  2  and  3)  has  a  greater  coverage  than  in  the  comparison  case 
(1),  price  fluctuations  are  smaller  for  him,  and  greater  for  his  partner, 
than  in  case  1.  A  high  reserve  ratio  gives  the  same  gold  flow  a  smaller 
effect  on  prices  than  a  lower  ratio. ^^ 


27.  In  our  former  example  it  took  place  slowly  outward  across  the  Wiirttemberg 
frontier,  because  reichmarks  were  valid  on  both  sides.  Beyond  the  national  frontier  it 
took  place  quickly,  because  of  dissimilarities  in  currency. 

28.  Temporary  differences  in  the  full  utilization  of  note  coverage  resemble  lasting 
differences  in  it.  These  differences  may  be  unintended.  With  a  50  per  cent  gold  cover- 
age in  each  of  two  countries  the  shipment  of  1,000  marks  in  gold  may  cause  a  change 
of  2,000  marks  in  the  amount  of  notes  in  one  if  it  is  on  the  upswing,  in  the  other  of 
hardly  1,000  if  it  is  in  a  depression. 

29.  This  among  other  things  explains  the  slight  reaction  of  prices  in  gold  move- 
ments in  the  United  States  and  France,  where  the  actual,  if  not  the  legal,  gold  coverage 
of  notes  is  very  high  and,  in  addition,  deposits  in  central  banks  have  to  be  partly 


284 


Part  Three.     Trade 


It  forms  a  cushion  against  the  effects  of  cyclical  changes  origi- 
nating abroad  and  of  international  capital  movements.  It  moderates 
deflationary  crises  and  inflationary  upswings,  though  in  return  it 
prolongs  them.  Indeed,  it  even  mitigates  the  deterioration  of  the 
barter  terms  of  trade  of  the  debtor  (that  is,  his  increased  cost  of 
imports  compared  with  his  exports) .  For  we  do  not  get  the  same 
result  when  we  interchange  the  reserve  ratios  of  debtors  and  creditors 
(compare  cases  2  and  3) .  If  we  were  to  assume  that  in  case  2,  as  in 
case  3,  300  marks  in  gold  had  been  shipped,  and  that  prices  therefore 
fell  in  A  by  30  per  cent  and  rose  in  5  by  8  per  cent,  so  that  in  com- 
parison with  case  3  only  the  roles  of  A  and  B  had  been  interchanged, 
the  end  result  would  still  not  be  the  same.  In  contrast  with  the 
original  situation  (=  100) ,  in  case  2  the  prices  in  A  would  stand 
at  70  and  in  B  at  108,  or  54  per  cent  above  those  in  ^;  in  case  3  at 
92  in  A  and  130  in  B,  or  only  41  per  cent  above  those  in  ^.  If 
equilibrium  prevails  in  case  3;  that  is,  if  the  price  difference  is  just 
enough  to  cause  700  marks'  worth  more  exports  from  A  to  B,  which 
together  with  300  marks  in  gold  is  exactly  equal  to  the  amount  of 
the  debt;  then  the  export  surplus  in  case  2  would  necessarily  be 
more  than  700  marks.  The  price  change  therefore  went  too  far; 
less  than  300  marks  in  gold  would  suffice  to  compel  the  remaining 
transfer  of  goods.  Nevertheless  the  gold  shipment  is  large  enough 
to  raise  prices  in  B  by  44  per  cent  above  those  in  A,  instead  of  by 
only  41  per  cent  as  in  case  3. 

Interchange  between  a  country  with  paper  ^°  and  one  with  gold 
currency  takes  place  according  to  the  rules  that  prevail  with  different 
reserve  ratios.  Gold  shipments  are  reduced  to  a  minimum.^^  We 
have  already  discussed  the  different  price  fluctuations. 

Of  course  these  differences  are  only  temporary.    (1)   The  larger 


covered  by  gold.  The  great  accumulations  of  gold  in  these  countries  are  not  explained 
thereby,  since  according  to  the  table  it  is  not  the  creditor  whose  actual  coverage  is  far 
above  that  of  its  debtor  (Case  2)  who  receives  large  shipments  of  gold,  but  the  one 
that  has  a  debtor  also  with  a  high  coverage  (Case  5) .  In  addition  this  gold  should 
flow  back  to  the  country  whence  it  first  came. 

30.  Here  fixed  cover  excludes  an  exchange  stabilization  fund  consisting  of  monetary 
gold,  which  with  variable  reserve  ratios  moderates  price  level  changes  even  when  the 
country  formally  has  a  paper  currency. 

31.  The  same  is  true  when  paper  currency  is  associated  with  variable  exchange 
rates.  If  the  debtor  country  has  a  gold  currency,  whereas  in  the  creditor  country  the 
price  rise  includes  also  the  commodity  gold,  gold  will  flow  temporarily  to  the  latter 
from  the  debtor  country  and  from  other  countries  as  well.  Conversely,  when  the 
debtor  country  has  a  paper  currency,  so  that  its  price  fall  includes  that  of  gold  too, 
commercial  gold  will  flow  into  the  creditor  country  and  into  other  countries  with  a 
fixed  gold  price. 


I 


Self-Regulation  285 

the  gold  shipments  and  therefore  the  smaller  the  price  and  com- 
modity movements  at  first,  the  longer  will  these  movements  persist 
before  the  preliminary  transfer  has  been  completed  entirely  in  goods. 
Thus  higher  note  coverage  does  7iot  decrease  the  necessary  transfer 
of  goods,  hut  merely  distributes  it  in  time.  As  a  result,  the  terms 
of  trade  of  the  debtor  remain  unfavorable  longer,  the  less  they 
deteriorate  at  first  because  of  large  gold  shipments.  This  means 
however,  that  the  same  quantity  of  goods  can  be  transferred  at 
lower  cost  on  the  whole  when  the  transfer  is  distributed  over  several 
economic  periods.  Thus  higher  note  coverage  lowers  the  cost  of 
preliminary  transfer.  (2)  This  is  not  of  much  importance,  of 
course,  as  long  as  these  costs  are  made  good  in  the  reaction.  But 
with  different  constructions  of  currency  this  need  no  longer  be 
invariably  the  case.  Consider  once  more  situations  2  and  3  in  Table 
16.  With  the  preliminary  transfer  the  terms  of  trade  of  A  deteriorate 
more  (price  difference  44  per  cent)  than  they  improve  in  the  reaction 
(price  difference  41  per  cent)  .^-  Accordingly,  the  statement  that 
higher  note  coverage  decreases  transfer  costs  has  a  truer  meaning 
than  would  appear  at  first  sight.  In  the  final  judgment  it  should 
be  remembered,  however,  that  the  higher  note  coverage,  too,  had 
to  be  accumulated  at  some  time,  with  transfer  losses  or  the  fore- 
going of  transfer  gains.  When  this  process,  which  has  generally 
occurred  far  in  the  past,  is  taken  into  account  also,  it  turns  out 
that  in  the  final  analysis  the  construction  of  a  currency  is  immaterial 
for  the  transfer.^^  If  the  past  is  disregarded,  however,  the  possibility 
cannot  be  rejected  that  despite  the  cost  in  interest  of  a  large  gold 

32.  A  and  B  must  be  imagined  as  interchanged  in  case  3  of  the  table  since  we  are 
supposed  to  be  dealing  with  the  same  participants  as  in  case  2,  only  with  transfer  in 
the  other  direction. 

33.  In  common  with  Lutz,  F.  W.  Meyer  ("  Devisenbewirtschaftung  als  neue  Wah- 
rungsform,"  Weltwirtschaftliches  Archiv,  XLIX  [1939],  415-471)  has  skillfully  defended 
the  thesis  that  the  gold  standard  could  no  longer  function  today  because,  among  other 
things,  countries  often  endeavor  to  sterilize  the  effects  of  gold  movements  out  of  cyclical 
considerations.  In  other  words,  they  act  as  though  their  reserve  ratios  were  consider- 
ably higher.  Now  although  this  results  in  larger  gold  shipments,  most  of  the  gold, 
even  with  protracted  unilateral  payments,  soon  flows  back  again  to  the  debtor,  whose 
prices  compared  with  those  of  the  creditor  and  in  contrast  with  the  prevailing  view, 
need  fall  less  than  if  gold  movements  could  affect  the  credit  structure  (see  Table  16)  . 
Basically  it  remains  true  nevertheless  that  the  construction  of  a  currency  (and  the 
sterilization  of  gold  movements  means  only  a  supplementary  change  in  this  construc- 
tion) is  immaterial  for  the  transfer  in  the  final  analysis.  A  policy  of  sterilization 
becomes  dangerous  only  when  it  attempts  also  to  neutralize  the  shift  in  purchasing 
power  proper  (not  only  its  multiple  effect  on  the  credit  structure)  ;  that  is,  when  it 
tries  to  prevent  the  origin  of  the  waves  of  purchasing  power  that  bring  about  actual 
transfer. 


286  Part  Three.     Trade 

reserve,  price  fluctuations  and  transfer  costs  hit  poor  countries  very 
much  harder  than  rich  ones. 

(cc)  Summary.  With  different  monetary  standards  (that  is, 
when  there  are  various  local  monies  that  are  only  partially  covered 
by  international  means  of  payment) ,  even  those  wholly  uncon- 
cerned in  a  transfer  (the  entire  debtor  and  creditor  country) 
co-operate  at  first  with  the  individual  economies  concerned  (debtors 
and  creditors)  in  making  the  transfer.  The  central  bank  of  the 
debtor  must  make  the  necessary  international  money  available  on 
the  payment  date,  and  with  a  fixed  reserve  ratio  this  can  be  done 
only  if  it  recalls  or  devalues  a  certain  amount  of  its  local  money. 
Both  courses  release  part  of  its  international  money,  one  by  de- 
creasing the  amount  of  local  money  to  be  covered,  the  other  by 
increasing  the  value  of  covering  international  money.  Both  provide 
it,  in  addition,  with  more  international  money  by  reducing  prices 
in  the  region  where  its  local  money  circulates  compared  with  those 
abroad,  thus  increasing  the  export  of  goods.  Compared  with  the 
second  (additional  exports) ,  the  first  source  of  gold  (freed  cover) 
flows  more  abundantly  the  higher  coverage,  especially  its  own.  With 
fixed  reserve  ratios  the  creditor  bank  must  support  these  endeavors 
of  the  debtor  bank.  All  these  events  are  repeated  in  the  opposite 
direction  during  the  reaction  and  leave  no  permanent  effect. 

3.     APPLICATION     OF     THE     NEW     THEORY 

Our  train  of  thought  carries  such  wide  implications,  yet  corre- 
sponds so  little  with  the  traditional  view,  that  it  may  be  good  to 
apply  it  to  a  few  important  examples. 

(aa)  Do  International  Obligations  of  a  Part  Mean  Injury  to 
the  Whole?  Does  Stuttgart,  in  our  preceding  example,  reduce  the 
foreign  exchange  for  the  whole  country  by  its  payment  abroad? 
Does  it  shift  the  costs  of  transfer  to  others?  The  old  theory  of 
international  trade,  which  regarded  the  preliminary  transfer  as  the 
sole  and  final  one,  would  have  to  answer  in  the  affirmative.  Unques- 
tionably it  is  the  function  of  an  increase  in  the  German  discount 
rate  to  expedite  the  transfer  by  drawing  in  also  those  who  are  not 
concerned  in  it;  that  is,  all  those  within  the  sphere  of  influence  of 
the  Reichsbank,  not  only  those  situated  in  the  Stuttgart  wave  of 
falling  prices.  It  worsens  the  barter  terms  of  trade  also  for  those 
who  either  have  already  shifted  their  share  in  the  loss  of  purchasing 
power  to  others  or  who,  with  a  uniform  currency,  would  have  had 
nothing  at  all  to  do  with  the  transfer.    But  we  now  know  that  this 


k 


Self-Regulation  287 

deterioration  is  only  temporary,  and  that  it  will  be  compensated 
later  by  an  equally  great  improvement.  The  contributions  of  non- 
participants  in  the  transfer  are  not  permanent.  The  whole  is  not 
burdened  by  the  acts  of  individuals. 

(bb)  The  Results  of  Transfer  Aid  for  Those  That  It  Favors. 
In  contrast  to  the  situation  where  Paris  and  Stuttgart  lie  within  an 
area  in  which  the  same  simple  metal  currency  is  valid  and  nothing 
occurs,  therefore,  save  the  final  transfer,  additional  price  fluctuations 
appear  in  Stuttgart  also.  The  smaller  the  sphere  of  influence  of  the 
central  issuing  bank,  the  sharper  are  these  fluctuations.  If  Wiirttem- 
berg  had  still  had  its  own  issuing  bank  and  had  sent  gold  directly 
to  London,  the  rise  in  the  Wiirttemberg  discount  rate  would  have 
been  much  greater  than  in  that  of  the  Reichsbank,  because  the  same 
amount  of  gold  would  have  meant  for  little  Wiirttemberg  a  dispro- 
portionately greater  loss  than  for  the  whole  country.  Compared 
with  this  situation  (case  A) ,  the  co-operation  of  the  entire  country 
(case  B)  has  moderated  the  price  fluctuations  in  Wiirttemberg.^* 
Hence  in  case  B  prices  in  Wiirttemberg  are  higher,  and  in  the  rest 
of  the  country  lower,  than  in  case  A.  As  a  consequence  it  takes 
longer  for  Wiirttemberg  to  achieve  the  export  surplus  required  even 
for  the  preliminary  transfer.  The  co-operation  of  the  entire  country 
does  not  relieve  Wiirttemberg  of  the  preliminary  transfer,^^  but 
facilitates  this  transfer  in  so  far  as  it  helps  to  spread  it  over  a  longer 
period  of  time.  Prices  in  Wiirttemberg  have  to  remain  lower  for  a 
longer  time,  though  the  decline  is  less.  Nevertheless,  even  in  case 
B  they  are  still  below  German  prices  as  a  whole:  (a)  because  of 
decreased  purchasing  power,  and  [h)  because  of  a  restriction  in 
bank  credits  consequent  upon  the  decreased  circulation  of  notes  due 
to  this  decline  in  purchasing  power.  This  restriction  in  bank  credits 
is  in  addition  to  the  general  national  restriction,  which  is  associated 
with  a  reduction  in  the  gold  reserve. 

(cc)  The  Extent  of  the  Preliminary  Transfer.  For  various 
reasons  the  preliminary  transfer  does  not  assume  the  proportions  of 
the  final  one. 

1.  It  does  not  take  place  if  debtors  and  creditors  make  early 
arrangements   in   anticipation  of  payment,   which   unintentionally 

34.  Unless  similar  disturbances  started  simultaneously  in  all  parts  of  the  country. 
As  a  rule,  however,  the  larger  the  currency  area  (at  least  until  it  includes  about  half 
the  world) ,  the  more  of  these  will  be  opposite  and  compensatory. 

35.  For  so  far  as  deposit  money  exists  such  a  preliminary  transfer  still  remains  to 
be  carried  out  between  Wiirttemberg  and  the  remainder  of  the  country. 


288  Part  Three.     Trade 

provide  the  debtor  bank  with  additional  foreign  exchange  until  the 
date  of  settlement.^®  If  we  disregard  capital  movements  because 
they  merely  postpone  the  problem,  the  debtor  must  bring  about  an 
export  surplus  of  the  size  of  the  payment.  This  may  be  done  by 
decreased  buying  (his  imports) ,  as  when  he  keeps  a  smaller  stock 
on  hand;  restriction  of  his  enterprise;  relinquishment  of  plans  to 
enlarge  his  factory,  and  the  like;  and  by  increasing  his  exports. 
The  former  lowers  wages  and  the  prices  of  imported  goods;  the 
latter,  the  prices  of  the  debtor's  products. 

In  expectation  of  payment  the  creditor  also  will  make  certain 
arrangements.  He  will  install  new  machines,  hire  workers,  and  order 
an  addition  to  his  building.  This  will  raise  somewhat  the  prices  of 
his  imports,  and  local  wages  in  particular,  even  before  the  actual 
payment.  Thanks  to  this  anticipatory  behavior  on  both  sides  there 
is,  on  the  one  hand,  a  German  export  surplus  in  consequence  of 
the  mere  shift  in  purchasing  power;  for  example,  because  the  debtor 
restricts  among  other  things  his  purchase  of  goods  that  formerly 
were  imported  into  Germany.^^ 

On  the  other  hand,  price  waves  begin  their  course,  which  is 
accompanied  by  a  gradual  transfer  of  goods,  even  before  the  transfer 
of  cash  is  to  be  made.  It  is  important  to  note  that  this  need  not 
necessarily  be  a  final  transfer;  that  is,  an  equalization  of  increased 
and  decreased  purchasing  power.  As  we  have  already  seen,  the 
movement  of  the  waves  of  purchasing  power  is  nothing  but  the 
result  and  cause  of  a  lasting  transfer  of  goods.  It  might  be  called 
an  "  advancing  wave  transfer."  As  soon  as  the  wave  of  price  reduc- 
tions, or  probably  in  this  case  merely  its  forerunner,  has  passed 
the  national  frontier,  the  transfer  of  goods  is  to  this  extent  com- 
pleted for  Germany,  although  the  final  equalization  may  not  occur, 
perhaps,  until  later,  and  far  from  the  frontier,  in  Lorraine  or  even 
deeper  in  France.  So  far  as  shifts  in  purchasing  power  and  price 
waves  caused  a  final  transfer  of  goods  across  the  German  frontier, 
a  certain  amount  of  money  is  already  available  on  the  date  of  pay- 
ment, and  to  this  extent  a  "  preliminary  transfer  "  is  superfluous.^^ 

36.  Applied  to  our  former  example,  the  preparation  for  (Stuttgart)  or  expectation 
of  (Paris)  a  transfer  of  cash  increases  the  supply  of  foreign  exchange  in  Berlin,  and 
only  with  the  remainder  of  its  demand  for  foreign  exchange  does  Stuttgart  raise  the 
rate  of  exchangs  for  the  franc  until  it  reaches  the  upper  gold  point. 

37.  In  countries  that  specialize  in  the  production  of  one  or  a  few  goods,  as  is  often 
the  case  in  South  America  for  example,  a  falling  off  in  the  demand  for  one  of  these 
exports  may  automatically  cause  a  decrease  in  imports.  See  H.  Backe,  Urn  die  Nah- 
rungsfreiheit  Europas    (Leipzig,  1942) ,  p.  75. 

38.  Strictly  speaking,  therefore,  even  in  a  final  transfer  of  goods  one  must  distin- 


Selj-Begvlation  289 

2.  The  preliminary  transfer  can  be  replaced  to  a  certain  extent 
by  short-term  capital  movements.  These  not  only  postpone  the 
transfer  problem  temporarily,  as  followed  from  the  classical  view, 
but  obviate  the  (strictly  speaking)  superfluous  preliminary  transfer. 
This  is  desirable  because  of  the  unfortunate  secondary  effects  of 
shifts  in  the  price  levels.  The  following  types  of  credit  have  this 
result:  (I)  Those  based  on  a  shift  in  purchasing  power  or  the  waves 
of  interest  to  which  it  gives  rise.  The  credits  must  expire  as  soon 
as  the  reaction  would  have  set  in.  In  so  far  as  this  serves  to  discharge 
the  credits  (at  most  up  to  half  the  debt) ,  the  preliminary  transfer 
becomes  superfluous.  (2)  Credits  between  central  banks,  except 
when  not  only  is  the  preliminary  transfer  thereby  avoided  but  the 
effects  of  waves  of  purchasing  power  are  compensated  in  addition. 
Otherwise  preliminary  transfer  would  not  be  avoided,  but  merely 
postponed.  In  our  example  either  the  credit  must  not  exceed  950 
marks,  else  the  Reichsbank  would  be  able  to  bring  the  1,000  marks 
withdrawn  from  circulation  in  Stuttgart  back  into  circulation  by 
granting  an  equal  amount  of  new  credits;  or  the  1,000  marks  can 
be  credited  in  full  if  Berlin  withdraws  them  from  circulation  and 
sterilizes  them,  and  Paris,  nevertheless,  pays  them  out  to  the  buyer.^^ 
The  credit  must  expire  as  soon  as  one  of  the  two  waves  of  falling 
prices  passes  the  German  frontier,  thus  providing  an  additional 
amount  in  foreign  exchange  of  1,000  gold  marks. *"  (3)  Partial 
crediting  of  the  debt  through  the  creditor  (payment  by  install- 
ments) .  With  continuing  payments  a  preliminary  transfer  is  neces- 
sary only  until  the  first  price  waves  have  reached  the  frontier.*^ 
Then  the  yield  of  foreign  exchange  from  the  passage  of  price  waves 
beyond  the  frontier  is  sufficient  to  make  good  the  current  transfer 


guish:  (1)  between  a  mere  "  advancing  wave  transfer "  and  a  final  equalization  of 
increased  and  decreased  purchasing  power  (concluding,  or  final,  transfer  of  goods  in 
the  narrow  sense)  ;  and,  (2)  in  both  cases  between  such  a  transfer  within  and  beyond 
currency  boundaries. 

39.  Example:  obligatory  clearing  credits.  See  my  article,  "  Die  Lehre  vom  Transfer— 
neu  gefasst,"  Jahrbiicher  fur  Nationalokonomie,  CLIV    (1941),  400  f. 

40.  This  recalls  the  procedure  employed  with  the  reparations  payments,  except  that 
then  the  tribute  money  collected  by  the  Reichsbank  did  not  have  to  be  sterilized— upon 
which  everything  depended. 

41.  If  payments  are  repeated  at  sufficiently  short  intervals  the  waves  become  a  con- 
tinuous price  drop.  The  price  differential  around  health  resorts  during  their  season, 
for  example,  is  of  this  type.  The  high  prices  in  such  places  result  not  only  from  the 
influx  of  purchasing  power,  however,  but  also  from  the  fact  that  their  season  is  very 
short.  It  is  also  important  that  production  for  their  own  consumption,  like  that  in 
towns  populated  by  rentiers  is  comparatively  small,  so  that  their  supply  areas  have  to 
be  greatly  extended  during  the  season. 


2()0 


Part  Three.     Trade 


of  cash.  From  this  moment  on  the  regions  that  are  not  concerned 
are  eliminated  again  from  the  transfer  mechanism.  The  reaction 
does  not  follow,  of  course,  until  payments  have  ceased.  Unlike  those 
described,  such  credit  movements,  which  are  due  to  the  discount 
policies  of  central  banks,  are  not  a  substitute  for  but  only  a  special 
form  of  the  preliminary  transfer.^^ 

3.  If  some  waves  of  purchasing  power  pass  beyond  the  German 
frontier  after  the  due  date,  but  before  all  German  gold  has  returned, 
an  appropriate  amount  of  gold  serves  to  pay  for  the  German  exports 
which  have  increased  with  that  passage.  To  this  extent  the  export 
surplus  thus  disappears  because  of  the  relative  change  in  the  price 
level.  The  interjerence  subsequently  reduces  the  extent  of  the  pre- 
liminary transfer  of  goods,  and  consequently  also  the  reaction.*^ 

(dd)  Is  the  Transfer  Aid  Necessary?  When  the  legal  or  eco- 
nomically advisable  reserves  are  fully  used  in  the  creation  of  notes 
or  deposits,  the  bank  authorities  cannot  chose  whether  or  not  to 
co-operate  in  the  preliminary  transfer.  With  a  reduction  of  the 
reserve  they  must  raise  the  discount  rate.  If,  on  the  other  hand, 
the  reserves  are  sufficient,  so  that  both  central  banks  can  sterilize  *^ 
the  gold  movements,  the  situation  is  exactly  as  with  a  purely  metallic 
currency:  The  preliminary  cash  transfer  is  not,  nor  need  it  be, 
associated  with  any  sort  of  transfer  of  goods.  It  is  accomplished 
simply  out  of  the  excess  reserves,  and  the  circulation  of  money  is 
decreased  only  by  those  means  of  payment  that  are  withdrawn  from 
circulation  when  the  debtor  accumulates  the  amount  to  be  paid. 

It  is  not  quite  so  easy  to  judge  the  absence  of  the  transfer  aid 
when  only  the  creditor,  but  not  the  debtor,  can  sterilize  gold  move- 
ments; that  is,  Avhen  these  lead  to  a  fall  in  the  debtor's  price  level. 
This  drop  results  in  a  smaller  export  surplus  than  if  prices  in  the 
creditor  country  had  risen  at  the  same  time.    Consequently  a  larger 

42.  See  "  Die  Lehre  vom  Transfer— iieu  gefasst,"  Jahrbiicher  fiir  Nationalokonomie, 
CLIV   (1941)  ,  391  f. 

43.  See  my  article  "  Um  eine  neue  Transfertheorie.  Zur  Verteidigung  der  alten 
Lehre  durch  Fritz  Meyer,"  Jahrbiicher  fiir  Nationalokonomie,  1943,  pp.  23-25,  a  reply 
to  Fritz  Meyer,  "  Eine  neue  Transfertheorie?  "  Archiv  fiir  Wirtschaftsplanung,  I  (1941) , 
171-180. 

44.  It  is  only  reasonable  to  prevent  a  shift  in  price  levels  by  foregoing  a  change  in 
the  discount  rate,  but  not  to  prevent  price  waves  by  open  market  operations.  Moreover, 
it  would  be  a  mistake  to  believe  that  the  effect  of  an  influx  of  gold  on  purchasing 
power  can  always  be  compensated  by  issuing  government  bonds  instead  of  bank  notes. 
If  the  economy  wants  more  money,  credit  will  be  created  to  the  limits  of  possibility, 
the  bank  discount  rate  will  rise  and  attract  foreign  money,  more  gold  will  flow  in, 
and  it  will  become  increasingly  difficult  to  counteract  its  effects  by  issuing  more  bonds, 
because  the  prices  of  previous  issues  have  fallen. 


Sdf-RegulalioTi  291 

part  of  the  preliminary  transfer  will  consist  at  first  of  gold,  and  a 
smaller  part  of  goods,  despite  a  sharper  drop  in  prices.  The  steriliza- 
tion policy  of  the  creditor  hurts  the  debtor  through  the  unfortunate 
effects  of  such  a  particularly  great  and  lasting  fall  in  prices.  In  the 
case  of  large  sums  the  severity  of  the  price  decline,  and  with  it  the 
success  of  the  preliminary  transfer  depends  essentially  upon  whether 
or  not  the  central  bank  of  the  creditor  provides  transfer  aid. 

(ee)  Whom  Do  Transfer  Costs  Affect?  The  advance  of  both 
waves  of  purchasing  power  is  associated  with  shifts  in  prices,  and 
hence  in  incomes,  that  are  partly  their  result  and  partly  their  cause. 
We  shall  call  them  "  transfer  costs  "  and  "  transfer  gains."  As  for  the 
two  parties  chiefly  concerned,  two  cases  must  be  distinguished:  (1) 
If  debtor  and  creditor  are  pure  consumers,  that  is,  if  we  deal  with 
payment  without  an  immediate  offsetting  payment,  the  effects  of 
a  transfer  are  exhausted  by  a  temporary  fall  in  prices  where  the 
debtor  reduces  his  purchases,  and  a  rise  where  the  creditor  buys 
more.  All  purchases  become  cheaper  for  the  payer  and  dearer  for 
the  payee.  The  debtor  makes  a  transfer  gain,  the  creditor  suffers 
a  loss.  Their  suppliers  are  affected  in  the  opposite  way.  (2)  It  is 
different  when  those  principally  concerned  are  themselves  producers 
and  a  debt  for  goods  is  to  be  paid,  as  was  assumed  in  connection 
with  Fig.  57.  Then  it  is  probable  that  the  debtor  will  bear  a  transfer 
burden.  For  he  has  bought  at  a  higher  price  from  the  creditor  B3, 
though  more  cheaply  from  his  former  supplier  B,  as  set  forth  above, 
and  he  will  reduce  his  own  prices  in  order  to  raise  the  additional 
amount.  Conversely,  the  creditor  will  make  a  transfer  gain,  which 
will  be  limited,  however,  by  the  fact  that  his  increased  demand 
makes  the  services  of  his  workers  and  sellers  more  expensive.  The 
change  in  the  selling  prices  of  those  chiefly  concerned  diminishes, 
though  in  small  measure,  the  losses  or  profits  of  their  sellers  in  so 
far  as  these  in  turn  buy  from  them.  Even  for  those  chiefly  con- 
cerned, this  business  connection  means  too  little  for  the  change  in 
purchasing  power  of  their  workers  and  sellers  to  be  noticeable  at 
first.  With  time,  of  course,  both  will  shift  part  of  their  loss  or  gain 
in  purchasing  power  to  others  in  the  manner  already  described, 
thereby  diminishing  their  disadvantage  or  advantage.  At  the  same 
time,  though  to  a  smaller  degree,  the  price  movement  will  be  passed 
on  to  the  regular  customers  of  those  chiefly  concerned,  which 
increases  their  transfer  gains  or  losses.*^   The  remainder  taking  part 

45.  The  severity  of  the  repercussions  varies  according  to  how  closely  and  elastically 
business  is  connected  with  the  source  of  the  movement.  It  is  probable  that  their 
strength  will  decrease  with  distance  from  it. 


2()2 


Part   Three.     Trade 


in  the  advancing  wave  transfer  will  be  less  affected  by  the  losses 
and  gains  the  farther  removed  they  are  iTom  the  points  of  origin, 
for  price  changes  decrease  with  distance,  as  we  have  seen.  But  it  is 
not  true  that  all  those  in  the  region  of  a  wave  of  rising  prices  will 
make  transfer  gains  and  all  those  in  other  regions  "\vill  undergo 
transfer  losses.  If  the  environs  of  Paris  and  Stuttgart  are  divided 
into  rings  those  buyers  in  every  ring  about  Stuttgart  who  made 
the  advance  possible  will  gain,  and  the  sellers  who  have  to  force 
the  advance  will  lose.  Conversely  around  Paris.  Now  as  almost 
everyone  is  both  buyer  and  seller,  he  makes  transfer  gains  only 
when  he  loses  less  by  the  cheapening  of  his  own  goods  than  he  gains 
through  the  cheapening  of  other  goods.  This  is  the  case  with  Stutt- 
gart in  all  except  the  two  innermost  rings,  which  include  the  debtor 
and  his  suppliers,  since  the  transfer  costs  decrease  from  ring  to  ring 
and  buyers  thus  gain  the  higher  transfer  costs  from  the  ring  pre- 
ceding their  own,  whereas  sellers  bear  the  lower  costs  of  advance 
to  the  next  ring.  The  sum  of  these  net  gains,  which  decrease  with 
distance,  is  equal  to  the  loss  sustained  by  the  suppliers  of  the  debtor. 

The  situation  at  the  German  frontier  remains  to  be  clarified. 
Buyers  in  the  Germ-an  frontier  ring  gain  from  Germans,  that  is,  from 
sellers  in  the  preceding  ring,  whereas  sellers  lose  to  Frenchmen, 
that  is,  to  buyers  in  the  French  frontier  ring.  Thus  in  the  German 
frontier  ring,  as  in  all  others,  there  is  a  transfer  gain,  but  for 
Germany  as  a  whole  a  transfer  loss  results,  though  it  is  not  very 
great  because  the  frontier  lies  far  away  from  Stuttgart.*^  In  contra- 
distinction to  political  frontiers,  no  income  shifts  appear  at  all  on 
economic  frontiers,  where  the  two  waves  of  purchasing  power  meet, 
because  here  the  final  settlement  is  completed  without  changes  in 
price. 

One  more  significant  error  in  the  old  theory  remains  to  be 
corrected.  In  so  far  as  the  creditor  buys  simply  what  the  debtor 
has  relinquished,  the  transfer  of  goods  was  thought  to  succeed 
through  mere  transfer  of  purchasing  power  without  change  of  price. 
This  argument  disregards  the  importance  of  distance.  In  Fig.  56, 
page  — ,  let  BA^  be  the  radius  of  the  former  supply  area  of  the 
debtor,  and  let  J5,/ii  be  the  same  for  the  creditor.  Because  of  the 
transfer  of  purchasing  power,  prices  fall  in  B.,  whereas  they  stiffen 
in  ^1.  The  new  price  cones  are  hatched.  The  region  between  Ai 
and  A..,  which  formerly  supplied  B>,  does  indeed  fall  to  the  creditor; 

46.  The  old  theory  recognized  only  this  loss  at  the  fiontier,  and  overestimated  it 
because  it  was  equated  with  tlie  losj  of  the  seller  in  the  innermost  ring.  Moreover,  it 
confused  the  losses  during  preliminary  transfer,  later  made  good,  with  the  final  losses. 


Self-Regulation  293 

but  only  at  one  single  point  C  is  the  price  received  by  the  seller 
still  the  old  one.*^  To  the  right  of  it  the  sellers  lose,  to  the  left  of 
it  they  gain,  exactly  as  we  have  concluded  in  general  for  regions 
with  a  loss  or  gain  in  purchasing  power. 

(ff)  Significance  of  the  Size  of  a  Country.  All  bank  customers, 
and  especially  those  of  the  central  bank,  constitute  a  transfer  com- 
munity, since  means  of  payment  circulate  among  them  that  are 
invalid  with  outsiders.  The  smaller  such  a  community  is,  the  more 
is  it  at  first  affected  by  a  transfer,  but  because  of  the  compensatory 
effect  of  the  reaction  this  fact  can  be  of  consequence  only  as  a  result 
of  frictional  difficulties.  For  it  is  not  countries  or  service  areas  of 
banks  that  take  part  in  exchange  and  are  affected  in  the  end  by  its 
mechanism,  but  individual  economic  units.  Geographic  differences 
prevail  eventually  against  movements  that  for  technical  reasons  are 
at  first  nationwide  [see  (bb)  ]. 

(gg)  Depreciation.  Like  a  change  in  the  discount  rate  of  the 
central  bank,  a  change  in  the  exchange  rate  affects  an  entire  country 
even  when  caused  by  only  a  part  of  it.  Suppose  that  upon  repayment 
of  a  large  loan  by  a  Berlin  firm  to  a  London  banking  house,  the 
Reichsbank  prefers  depreciating  the  exchange  rate  by  20  per  cent 
to  a  sharp  increase  in  the  discount  rate.  As  soon  as  the  preliminary 
transfer  has  been  completed  the  exchange  rate  goes  up  again  to  its 
former  level,  and  even  higher  during  the  reaction.  If  the  Reichsbank 
wished  to  maintain  the  lower  rate,  German  prices  would  have  to 
rise  instead.  When  through  depreciation  one  aims  merely  to  avoid 
such  price  fluctuations,  it  is  wrong  to  adhere  forever  to  the  lower 
rate  of  exchange. 

Let  us  compare  exchange  depreciation  to  facilitate  transfer  with 
the  results  of  a  depreciation  to  revive  the  economy.  If  a  20  per  cent 
depreciation  is  assumed  in  both  cases,  the  price  levels  will  eventually 
rise  by  20  per  cent  in  both.  But  what  will  happen  before  matters 
have  gone  this  far  is  decidedly  different.  (1)  According  to  extent: 
With  transfer  the  price  level  rises  in  the  reaction  by  as  much  as 
40  per  cent,  but  with  a  depreciation  for  cyclical  reasons  never  by 
more  than  20  per  cent.  (2)  According  to  direction:  With  transfer 
the  calculated  price  average  falls  at  first  because  of  the  wave  of 
lower  prices,  and  again  later  when  the  reaction  subsides  (from  40 
to  20  per  cent  above  the  old  level) ,  whereas  with  a  cyclical  revival 

47.  Only  when  the  supply  in  Aj^  is  very  large,  so  that  the  shift  in  demand  is 
expressed  solely  by  the  fact  that  Z?i  and  B„  are  now  supplied  in  different  proportions, 
will  no  price  change  occur. 


294 


Part  Three.     Trade 


and  without  the  necessity  of  a  reaction,  the  price  level  always  rises 
continuously.  (3)  Geographically:  The  manner  in  which  the  rise 
of  the  price  level  is  accomplished  is  the  same  in  both  cases,  to  be 
sure,  yet  instructive  enough  to  be  examined  more  closely  in  the  case 
of  a  depreciation  for  cyclical  reasons.  Depreciation  lowers  domestic 
prices  at  first  compared  with  those  abroad.  The  foreign,  and  with 
it  the  total  demand  increases;  so,  too,  do  prices  therefore  in  both 
domestic  and  foreign  currency.  But  they  do  not  rise  uniformly. 
As  a  rule,  though  not  necessarily,  the  smaller  exports  were  before 
depreciation  relative  to  domestic  sales,  the  less  important  will  be  the 
increase  in  foreign  dem.and  and  the  less  prices  need  rise  in  conse- 
quence. For  this  reason  the  price  rise,  and  with  it  the  revival  is 
regionally  quite  different  at  first,  but  with  time  it  is  diffused  from 
the  region  and  the  branches  of  business  first  affected,  to  all  equally. 
At  last,  if  we  disregard  secondary  cyclical  effects,  all  prices  except 
interest  rates  will  rise  in  the  same  proportion  as  the  rate  of  exchange 
has  been  lowered. 

This  second  phase  is  hard  to  demonstrate  in  concrete  cases, 
because  it  appears  so  late  that  new  events  distort  the  picture  again. 
The  first  phase,  however,  is  well  shown  by  the  example  of  the 
American  depreciation.  In  1935,  as  compared  with  1932,  the  year 
preceding  the  depreciation,  the  prices  of  such  typically  domestic 
goods  as  fuel  and  furniture  rose  least,  the  former  by  4^  per  cent.^^ 
Industrial  goods  of  which  a  few  were  exported  rose  more:  e.  g., 
textiles  by  29  per  cent.  The  greatest  increase  was  shown  by  agri- 
cultural products  with  a  high  export  quota;  cotton,  for  example,  of 
which  more  than  half  the  crop  is  exported,  rose  in  price  at  New 
Orleans  by  87  per  cent.^^  The  still  greater  increase  in  the  case  of 
wheat,  almost  none  of  which  was  exported,  was  caused  by  failure 
of  the  harvest.^"  Measures  to  limit  the  acreage  under  cultivation 
also  played  a  role,  though  not  a  decisive  one. 

Hence  depreciation  benefited  most  America's  great  depressed 
area,  the  cotton-raising  South  Avhich,  conversely,  had  been  hardest 
hit  earlier  by  the  depression.  The  situation  of  the  cotton  grower 
was  naturally  communicated  to  the  prices  of  the  goods  he  used,  but 
not  in  such  a  way  as  to  change  them  immediately  and  uniformly 
throughout  the  whole  United  States;  on  the  contrary,  they  reacted 
most  strongly  first  at  the  seat  of  the  cause.  Thus  up  to  1932  the 
retail  prices  of  food  had  fallen  33  to  37  per  cent  below  those  of  1929 

48.  See  U.  S.  Statistical  Abstract,  1936,  p.  299. 

49.  U.  S.  Department  of  Agriculture,  Agricultural  Statistics,  1936,  p.  83. 

50.  See  S.  E.  Harris,  Exchange  Depreciation    (Cambridge,  Mass.,  1936),  p.  341. 


Self-Regulation  295 

in  the  individual  census  regions  comprising  the  main  industrial  belt: 
New  England,  Middle  Atlantic,  East  North  Central.  By  comparison, 
they  had  fallen  in  the  cotton  belt,  i.  e.,  the  South  Atlantic,  East  South 
Central,  and  West  South  Central  States,  by  35  to  39  per  cent.  Con- 
versely, in  the  industrial  area  in  1935  they  were  15  to  20  percent  and 
in  the  cotton  belt  20  to  22  per  cent  above  those  of  1932." 

The  same  result  emerges  in  a  comparison  of  the  cost  of  living 
for  workers  in  six  cities  of  the  industrial  area  (Boston,  Buffalo, 
New  York,  Philadelphia,  Chicago,  and  Cleveland)  with  those  for 
six  in  the  cotton  belt  (Atlanta,  Houston,  Memphis,  Mobile,  New 
Orleans,  and  Savannah) .  Between  1929  and  1932  they  fell  20  to 
26  per  cent  in  the  industrial  area,  to  22  to  27  percent  in  the  cotton 
belt,  and  rose  3  to  6  per  cent  in  the  former  in  1932-1935  and  4  to 
10  per  cent  in  the  latter.^- 

It  must  not  be  forgotten,  however,  that  the  export  quota  merely 
determined  the  rate  at  which  the  prices  of  various  goods  eventually 
adapted  themselves  equally  to  the  depreciation.  With  transfer,  the 
price  average  adjusts  itself  in  the  described  manner  more  slowly 
and  among  regions  less  uniformly.  The  fault  lies  with  the  wave  of 
lowered  prices,  which  is  added  to  the  true  shift  in  price  level  and 
changes  the  arithmetical  average. 

First,  it  is  clear  that  the  original  price  fall  relative  to  other 
countries  in  the  part  of  Germany  affected  by  loss  of  purchasing 
power  (spreading  outward  from  Berlin  in  our  example)  is  greater 
by  the  effects  of  this  loss.  But  even  within  the  Berlin  economic  area 
there  are  differences.  In  the  first  place,  the  prices  of  the  repaying 
industries  decline.  Even  later,  when  the  price  drop  is  being  trans- 
ferred to  other  businesses,  a  difference  remains  compared  with  the 
debt-paying  branches.  The  change  in  local  prices  depends,  therefore, 
entirely  on  the  industries  of  the  place  concerned:  those  primarily 
affected  by  the  lower  prices,  those  only  moderately  affected,  or  those 
that  are  wholly  untouched.  The  price  level  of  the  Berlin  area  does 
not  fall  evenly,  but  by  separate  drops  here  and  there. 

Even  within  the  market  areas  of  the  industries  particularly 
affected  the  price  drop  is  not  uniform.  As  a  rule,  production  costs 
in  the  industries  concerned  have  to  fall  more  sharply  (though  not 
equally  in  all  branches)  than  shipping  costs,  which  also  depend 
upon  sales  in  other  businesses.    Consequently  prices  drop  by  the 

51.  Calculated  from  U.  S.  Bureau  of  Labor  Statistics,  Retail  Prices,  Serial  No.  R  384, 
pp.  8-9. 

52.  Calculated  from  U.  S.  Statistical  Abstract,  1935,  p.  298.    Original  data  from  the 
Bureau  of  Labor  Statistics. 


2g6  Part  Three.     Trade 

largest  percentage  at  the  site  of  production  and  less  sharply  on  the 
borders  of  the  market  area;  because  freight,  which  has  hardly 
decreased,  is  an  important  factor  there.  In  addition,  the  whole 
wave  of  lower  prices  eventually  draws  away  from  Berlin  and  flattens 
out  as  it  hits  other  places. 

Finally,  instead  of  paying  attention  to  these  local  differences,  let 
us  compare  the  calculated  average  for  the  economic  landscapes  of 
Germany  regardless  of  the  causes  of  its  change.  Although  German 
prices  as  a  whole  fall  at  first  compared  with  foreign  prices,  those  in 
Munich  rise  at  once  compared  with  those  in  Berlin,  if  we  regard 
Berlin  as  representative  of  the  part  of  Germany  affected,  and  Munich 
as  representative  of  the  temporarily  unaffected  part;  that  is,  not  yet 
reached  by  the  wave.  Gradually  the  depreciation,  which  for  no 
reason  at  all  has  lowered  Munich  export  prices  also  by  20  per  cent, 
leads  by  way  of  the  resulting  export  surplus  and  decline  of  imports 
to  the  restraining  rise  in  the  price  level  that  has  been  described 
above.  Penetrating  from  the  frontier  to  the  interior  of  Germany, 
it  equalizes  again  the  fall  in  the  exchange  rate  for  the  whole  country 
in  so  far  as  this  is  not  actually  affected  by  the  ebb  in  purchasing 
power  originating  in  Berlin;  and  later,  during  the  reaction,  more 
than  equalizes  it.  This  last  difference  in  price  levels  persists,  even 
though  between  changing  regions,  until  the  wave  has  receded  from 
Germany. 

From  all  this  it  follows  that  repayment  of  a  foreign  loan  first  raises 
and  then  lowers  the  German  price  level  on  the  average;  but  that 
within  Germany,  within  its  great  economic  areas,  within  individual 
small  market  areas,  and  even  within  single  enterprises  something 
entirely  different  takes  place. ^^  The  difference  is  not  merely  a  matter 
of  subtle  variations;  they  go  so  far  that  Munich  will  reverse  what 
started  in  Berlin.  This  example  shows  what  a  great  number  of 
differences  the  concept  "  general  price  level  "  conceals.  But,  to 
return  to  our  starting  point,  it  shows  above  all  that  a  depreciation 
due  to  a  transfer  works  quite  differently  from  a  depreciation  to 
revive  the  economy. 

Fluctuating  exchange  rates  present  the  transfer  theory  with  yet 
another  difficult  problem:  The  two  waves  of  purchasing  power  seem 
no  longer  equivalent  in  value  terms;  how,  then,  can  they  equalize 
one  another?  Suppose  1,000  marks  originally  equal  1,000  francs.  But 
because  of  exchange  depreciation  the  German  debtor  has  to  pay 

53.  Something  very  similar  is  to  be  seen  in  meteorology.  Within  widespread  weather 
conditions  every  street  and  every  "square  in  our  German  cities  often  maintains  its  own 
entirely  distinct  climate,  which  shares  with  varying  intensity  in  a  change  of  weather. 


Self-Regulation  297 

1,100  marks  for  1,000  francs.  On  the  other  hand,  with  the  higher 
exchange  rate  that  results  from  the  passing  of  the  ebb  in  purchasing 
power  across  the  border,  1,100  marks  might  now  correspond  perhaps 
to  1,300  francs.  An  ebb  in  purchasing  power  of  1,300  francs  and  a 
tidal  wave  of  only  1,000  francs  would  then  meet  in  France. 

But  as  a  rule  events  do  not  occur  in  this  way.  The  fate  of  the 
true  Stuttgart  ebb  in  purchasing  power  of  1,000  marks  and  of  the 
additional  Stuttgart  exchange  loss  of  100  marks  is  different.  The  ebb 
is  locally  limited,  whereas  the  corresponding  increase  in  purchasing 
power  ^*  among  exporters,  who  export  more,  and  importers,  who 
import  less,  is  distributed  throughout  all  Germany  and  raises  the 
price  level  everywhere.®^  Exchange  profits  and  losses  are  similarly 
distributed  spatially  and  the  Stuttgart  loss  is  generally  indistin- 
guishable from  the  others.  It  is  decisive  that  the  small  waves  of  ebb 
and  flood  that  arise  everywhere  in  Germany  because  of  the  altered 
exchange  rate  equalize  one  another  more  easily  than  do  the  general 
rise  in  level  and  the  local  Stuttgart  ebb.  Only  at  first,  when  the 
great  wave  has  just  begun  its  course,  do  the  ebb  and  the  excess 
purchasing  power  that  is  not  yet  absorbed  through  higher  prices, 
equalize  one  another.  The  greater  part  of  the  ebb,  hower,  will  reach 
the  national  frontier.  The  small  exchange  waves,  on  the  contrary, 
cancel  out  within  a  short  distance  luiless  the  Stuttgart  disturbance 
is  unusually  severe.  Thus  the  essential  processes  in  the  transfer  are 
the  same  with  fixed  and  fluctuating  exchanges. 

(hh)  Does  It  Make  Any  Difference  in  What  Currency  a  Debt 
Is  Payable?  Whether  in  that  of  the  creditor  or  the  debtor?  It  is 
obviously  immaterial  for  the  countries  concerned  whether  the 
creditor  or  the  debtor  starts  the  fluctuations  in  price  level  or  ex- 
change rate  in  the  process  of  changing  one  currency  into  another. 
With  a  fixed  exchange  rate  it  makes  no  difference  to  either,  but  with 
variable  rates  the  one  that  makes  or  receives  ^^  payment  in  foreign 
money  bears  the  exchange  loss. 

54.  It  does  not  leave  Germany,  as  would  be  the  case  with  a  fixed  exchange  rate 
through  the  shipment  or  the  destruction  the  money. 

55.  On  the  average  it  does  not  rise,  if  the  ebb  is  also  taken  into  account. 

56.  This  is  improbable,  however,  for  who  would  desire  payment  in  a  currency  that 
he  does  not  wish  to  spend?  But  so  far  as  the  statement  holds,  and  it  holds  especially 
for  foreign  deposits  in  banks,  it  is  true  that  fluctuating  exchanges  hinder  international 
capital  movements  because  of  the  exchange  risk  involved.  With  paper  currencies, 
therefore,  special  reasons  are  added  to  the  general  reasons  why  capital  is  less  mobile 
than  within  countries.  But  on  the  whole  one  can  agree  with  Ch.  R.  Whittlesey  ("  Inter- 
nationale Kapitalbewegungen  bei  gebundener  und  freier  Wahrung,"  Weltwirtschaft- 
liches  Archiv  XLIV  [1936])  that  the  restraining  effect  of  free  exchanges  on  the  inter- 
national movement  of  capital  has  been  greatly  exaggerated  in  the  past. 


2q8 


ParL   Three.     Trade. 


(ii)  Unilateral  Waves  of  Purchasing  Power.  A  local  upswing 
can  release  a  fl